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Clay Cordova (University of CHICAGO)
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Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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media:description>These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
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Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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name>Institut des Hautes Etudes Scientifiques (IHES)/name>
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media:description>These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
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Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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media:description>These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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name>Institut des Hautes Etudes Scientifiques (IHES)/name>
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media:description>1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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title>Max Metlitski - 3/4 Introduction to anomalies in condensed matter physics/title>
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author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
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published>2024-06-27T07:51:02+00:00/published>
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media:title>Max Metlitski - 3/4 Introduction to anomalies in condensed matter physics/media:title>
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media:thumbnail url="https://i2.ytimg.com/vi/Yl5tSGgjWYQ/hqdefault.jpg" width="480" height="360"/>
media:description>1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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title>Thomas Dumitrescu - 4/4 Generalized Symmetries and Phases of Gauge Theory/title>
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author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
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published>2024-06-27T07:49:00+00:00/published>
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media:description>These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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title>Thomas Dumitrescu - 3/4 Generalized Symmetries and Phases of Gauge Theory/title>
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author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
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media:group>
media:title>Thomas Dumitrescu - 3/4 Generalized Symmetries and Phases of Gauge Theory/media:title>
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media:thumbnail url="https://i1.ytimg.com/vi/0D8jeJMF2RM/hqdefault.jpg" width="480" height="360"/>
media:description>These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
media:community>
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title>Max Metlitski - 2/4 Introduction to anomalies in condensed matter physics/title>
link rel="alternate" href="https://www.youtube.com/watch?v=AxoYOGtZHzw"/>
author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
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media:title>Max Metlitski - 2/4 Introduction to anomalies in condensed matter physics/media:title>
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media:thumbnail url="https://i2.ytimg.com/vi/AxoYOGtZHzw/hqdefault.jpg" width="480" height="360"/>
media:description>1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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title>Thomas Dumitrescu - 2/4 Generalized Symmetries and Phases of Gauge Theory/title>
link rel="alternate" href="https://www.youtube.com/watch?v=SmVP1CK3NJA"/>
author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
/author>
published>2024-06-25T19:18:09+00:00/published>
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media:group>
media:title>Thomas Dumitrescu - 2/4 Generalized Symmetries and Phases of Gauge Theory/media:title>
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media:thumbnail url="https://i4.ytimg.com/vi/SmVP1CK3NJA/hqdefault.jpg" width="480" height="360"/>
media:description>These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
media:community>
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yt:videoId>grtEwGUeCo0/yt:videoId>
yt:channelId>UC4R1IsRVKs_qlWKTm9pT82Q/yt:channelId>
title>Max Metlitski - 1/4 Introduction to anomalies in condensed matter physics/title>
link rel="alternate" href="https://www.youtube.com/watch?v=grtEwGUeCo0"/>
author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
/author>
published>2024-06-24T18:33:41+00:00/published>
updated>2024-06-28T01:43:10+00:00/updated>
media:group>
media:title>Max Metlitski - 1/4 Introduction to anomalies in condensed matter physics/media:title>
media:content url="https://www.youtube.com/v/grtEwGUeCo0?version=3" type="application/x-shockwave-flash" width="640" height="390"/>
media:thumbnail url="https://i4.ytimg.com/vi/grtEwGUeCo0/hqdefault.jpg" width="480" height="360"/>
media:description>1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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yt:videoId>9pqtqyGtt3M/yt:videoId>
yt:channelId>UC4R1IsRVKs_qlWKTm9pT82Q/yt:channelId>
title>Thomas Dumitrescu - 1/4 Generalized Symmetries and Phases of Gauge Theory/title>
link rel="alternate" href="https://www.youtube.com/watch?v=9pqtqyGtt3M"/>
author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
/author>
published>2024-06-24T18:19:33+00:00/published>
updated>2024-06-24T18:33:12+00:00/updated>
media:group>
media:title>Thomas Dumitrescu - 1/4 Generalized Symmetries and Phases of Gauge Theory/media:title>
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media:thumbnail url="https://i2.ytimg.com/vi/9pqtqyGtt3M/hqdefault.jpg" width="480" height="360"/>
media:description>These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
media:community>
media:starRating count="26" average="5.00" min="1" max="5"/>
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entry>
id>yt:video:7tu4LeNS_tE/id>
yt:videoId>7tu4LeNS_tE/yt:videoId>
yt:channelId>UC4R1IsRVKs_qlWKTm9pT82Q/yt:channelId>
title>Langbing Luo - Logarithmic Sobolev inequalities on homogeneous spaces/title>
link rel="alternate" href="https://www.youtube.com/watch?v=7tu4LeNS_tE"/>
author>
name>Institut des Hautes Etudes Scientifiques (IHES)/name>
uri>https://www.youtube.com/channel/UC4R1IsRVKs_qlWKTm9pT82Q/uri>
/author>
published>2024-06-18T22:02:30+00:00/published>
updated>2024-06-23T20:40:20+00:00/updated>
media:group>
media:title>Langbing Luo - Logarithmic Sobolev inequalities on homogeneous spaces/media:title>
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media:thumbnail url="https://i4.ytimg.com/vi/7tu4LeNS_tE/hqdefault.jpg" width="480" height="360"/>
media:description>We consider sub-Riemannian manifolds which are homogeneous spaces equipped with a sub-Riemannian structure induced by a transitive action by a Lie group. The corresponding sub-Laplacian there is not an elliptic but a hypoelliptic operator. We study logarithmic Sobolev inequalities and show that the logarithmic Sobolev constant can be chosen to depend only on the Lie group acting transitively on such a space but the constant is independent of the action of its isotropy group. This approach allows us to track the dependence of the logarithmic Sobolev constant on the geometry of the underlying space, in particular we show that the constant is independent of the dimension of the underlying spaces in several examples. Based on joint work with M.Gordina.
Langbing Luo (UConn)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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yt:videoId>BbBN8rhHScU/yt:videoId>
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title>Masha Gordina - Dimension-independent functional inequalities on sub-Riemannian manifolds/title>
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Masha Gordina (UConn)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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title>Amandine Aftalion - La science au service de la performance des sportifs/title>
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media:thumbnail url="https://i3.ytimg.com/vi/zZ0CJGHFdJM/hqdefault.jpg" width="480" height="360"/>
media:description>Pourquoi les sprinteurs décélèrent-ils avant de passer la ligne d’arrivée ?
Pourquoi vaut-il mieux courir derrière quelqu’un ?
Comment ajuster au mieux sa vitesse pour faire le meilleur temps ?
Cela dépend de l’effort fourni, de l’énergie dépensée, de la motivation car l’être
humain n’est pas un robot et son mouvement est commandé par son cerveau.
À ces questions et quelques autres (Pourquoi la balle de golf a-t-elle des alvéoles ?
Pourquoi nage-t-on mieux légèrement sous l’eau), Amandine Aftalion répond en
s’appuyant sur des notions de physique et de mathématiques, présentées de
façon simple et agréable, et nous permet de mieux comprendre quelques règles
pour améliorer la pratique sportive.
Amandine Aftalion (CNRS, Centre d’analyse et de mathématiques sociales, EHESS)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===/media:description>
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++++ UPdate DAvidKanal SET tsc=1720166922 WHERE Cid="19762"
05.07.2024 10:08
01.01.1970 01:00
01.01.1970 01:00
Institut des Hautes Études Scientifiques (IHÉS)
10.06.2024 · 19:31:48 ···
10.06.2024 · 19:31:43 ···
30.04.2023 · 05:39:01 ··· 5 ··· ··· 75 ···
05.07.2024 · 10:08:42 ···
30.06.2024 · 10:08:39 ···
30.04.2023 · 05:39:01 ··· 5 ··· ··· 90 ···
1:: Clay Cordova - 4/4 Higher Symmetry in Particle Physics
01.01.1970 · 01:00:00 ··· 28.06.2024 · 20:25:43 ··· ··· ··· ··· ··· ··· These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
2:: Clay Cordova - 3/4 Higher Symmetry in Particle Physics
01.01.1970 · 01:00:00 ··· 28.06.2024 · 16:56:02 ··· ··· ··· ··· ··· ··· These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
3:: Clay Cordova - 2/4 Higher Symmetry in Particle Physics
01.01.1970 · 01:00:00 ··· 27.06.2024 · 20:49:50 ··· ··· ··· ··· ··· ··· These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
4:: Clay Cordova - 1/4 Higher Symmetry in Particle Physics
01.01.1970 · 01:00:00 ··· 27.06.2024 · 15:45:03 ··· ··· ··· ··· ··· ··· These lectures will focus on higher symmetry in the standard model and beyond, illustrating how new symmetry principles can be a powerful organizing tool for well motivated models of particle physics.
Clay Cordova (University of CHICAGO)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
5:: Max Metlitski - 4/4 Introduction to anomalies in condensed matter physics
01.01.1970 · 01:00:00 ··· 27.06.2024 · 15:44:41 ··· ··· ··· ··· ··· ··· 1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
6:: Max Metlitski - 3/4 Introduction to anomalies in condensed matter physics
01.01.1970 · 01:00:00 ··· 27.06.2024 · 07:51:02 ··· ··· ··· ··· ··· ··· 1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
7:: Thomas Dumitrescu - 4/4 Generalized Symmetries and Phases of Gauge Theory
01.01.1970 · 01:00:00 ··· 27.06.2024 · 07:49:00 ··· ··· ··· ··· ··· ··· These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
8:: Thomas Dumitrescu - 3/4 Generalized Symmetries and Phases of Gauge Theory
01.01.1970 · 01:00:00 ··· 25.06.2024 · 19:19:34 ··· ··· ··· ··· ··· ··· These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
9:: Max Metlitski - 2/4 Introduction to anomalies in condensed matter physics
01.01.1970 · 01:00:00 ··· 25.06.2024 · 19:18:49 ··· ··· ··· ··· ··· ··· 1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
10:: Thomas Dumitrescu - 2/4 Generalized Symmetries and Phases of Gauge Theory
01.01.1970 · 01:00:00 ··· 25.06.2024 · 19:18:09 ··· ··· ··· ··· ··· ··· These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
11:: Max Metlitski - 1/4 Introduction to anomalies in condensed matter physics
01.01.1970 · 01:00:00 ··· 24.06.2024 · 18:33:41 ··· ··· ··· ··· ··· ··· 1. General "definition" of topological phases and of invertible phases.
2. Illustration of invertible phases with a 1+1d Majorana chain and connection to continuum field theory (massive Majorana fermion).
3. Introduction of bordism invariance and classification of invertible phases.
4. If time allows, invertible phases with Z classification (Chern Simons response) as illustrated by 2+1d p+ip superconductor.
5. Phases protected by symmetry. Symmetry on the lattice.
6. In cohomology SPT and Dijkgraaf-Witten theories. If time allows, a detailed analysis of the 2+1D Levin-Gu bosonic Z 2 SPT.
Max Metlitski (MIT)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
12:: Thomas Dumitrescu - 1/4 Generalized Symmetries and Phases of Gauge Theory
01.01.1970 · 01:00:00 ··· 24.06.2024 · 18:19:33 ··· ··· ··· ··· ··· ··· These lectures will introduce higher-form and higher-group symmetries (as well as related concepts such as anomalies and SPTs) through the lens of gauge theory phases in 3+1 dimensions.
Thomas Dumitrescu (UCLA)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
13:: Langbing Luo - Logarithmic Sobolev inequalities on homogeneous spaces
01.01.1970 · 01:00:00 ··· 18.06.2024 · 22:02:30 ··· ··· ··· ··· ··· ··· We consider sub-Riemannian manifolds which are homogeneous spaces equipped with a sub-Riemannian structure induced by a transitive action by a Lie group. The corresponding sub-Laplacian there is not an elliptic but a hypoelliptic operator. We study logarithmic Sobolev inequalities and show that the logarithmic Sobolev constant can be chosen to depend only on the Lie group acting transitively on such a space but the constant is independent of the action of its isotropy group. This approach allows us to track the dependence of the logarithmic Sobolev constant on the geometry of the underlying space, in particular we show that the constant is independent of the dimension of the underlying spaces in several examples. Based on joint work with M.Gordina.
Langbing Luo (UConn)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
14:: Masha Gordina - Dimension-independent functional inequalities on sub-Riemannian manifolds
01.01.1970 · 01:00:00 ··· 18.06.2024 · 22:02:13 ··· ··· ··· ··· ··· ··· The talk will review recent results on gradient estimates, reverse Poincare and reverse log Sobolev inequalities on a class of sub-Riemannian manifolds. As for many of such setting curvature bounds are not available, we use different techniques. I will introduce the basics of sub-Riemannian manifolds including their metric structure. Joint work with F. Baudoin, L. Luo and R. Sarkar.
Masha Gordina (UConn)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
15:: Amandine Aftalion - La science au service de la performance des sportifs
01.01.1970 · 01:00:00 ··· 18.06.2024 · 22:01:53 ··· ··· ··· ··· ··· ··· Pourquoi les sprinteurs décélèrent-ils avant de passer la ligne d’arrivée ?
Pourquoi vaut-il mieux courir derrière quelqu’un ?
Comment ajuster au mieux sa vitesse pour faire le meilleur temps ?
Cela dépend de l’effort fourni, de l’énergie dépensée, de la motivation car l’être
humain n’est pas un robot et son mouvement est commandé par son cerveau.
À ces questions et quelques autres (Pourquoi la balle de golf a-t-elle des alvéoles ?
Pourquoi nage-t-on mieux légèrement sous l’eau), Amandine Aftalion répond en
s’appuyant sur des notions de physique et de mathématiques, présentées de
façon simple et agréable, et nous permet de mieux comprendre quelques règles
pour améliorer la pratique sportive.
Amandine Aftalion (CNRS, Centre d’analyse et de mathématiques sociales, EHESS)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
16:: Philippe Biane - Quantum Exclusion Process, Random Matrices and Free Cumulants
01.01.1970 · 01:00:00 ··· 10.06.2024 · 12:39:59 ··· ··· ··· ··· ··· ··· The Quantum Symmetric Simple Exclusion Process (QSSEP) is a model of quantum particles hopping on a finite interval and satisfying the exclusion principle. I will explain how free cumulants, which are quantities arising in free probability and random matrix theory, encode the fluctuations of the invariant measure of this process when the number of sites goes to infinity.
Philippe Biane (Laboratoire d'Informatique Gaspard Monge, Marne-la-Vallée)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
17:: Bertrand Eynard - Topological Recursion: a recursive way of counting surfaces
01.01.1970 · 01:00:00 ··· 10.06.2024 · 12:39:18 ··· ··· ··· ··· ··· ··· Enumerating various kinds of surfaces is an important goal in combinatorics of maps, enumerative geometry, string theory, statistical physics, and other areas of mathematics or theoretical physics. For example the famous Mirzakhani's recursion is about enumerating hyperbolic surfaces. It is often easier to enumerate planar surfaces, with the lowest topologies (disc, cylinder), and the question is how to enumerate surfaces of higher genus and with more boundaries. Many of the surface enumeration problems, satisfy a universal recursion, known as the "topological recursion", which, from the enumeration of discs and cylinders, gives all the other topologies. Moreover this recursion has many beautiful mathematical properties by itself, and allows to make the link with other areas of mathematics and physics, in particular integrable systems, random matrices, and many others.
Bertrand Eynard (Institut de physique théorique, CEA Saclay)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
18:: Guillaume Aubrun - Entangleability of Cones
01.01.1970 · 01:00:00 ··· 10.06.2024 · 12:37:37 ··· ··· ··· ··· ··· ··· We solve a long-standing conjecture by Barker, proving that the minimal and maximal tensor products of two finite-dimensional proper cones coincide if and only if one of the two cones is generated by a linearly independent set. Here, given two proper cones $C1, C2$, their minimal tensor product is the cone generated by products of the form $x1 \otimes x2$, where $x1 \in C1$ and $x2 \in C2$, while their maximal tensor product is the set of tensors that are positive under all product functionals $f1 \otimes f2$, where $f1$ is positive on $C1$ and $f2$ is positive on $C2$. Our proof techniques involve a mix of convex geometry, elementary algebraic topology, and computations inspired by quantum information theory. Our motivation comes from the foundations of physics: as an application, we show that any two non-classical systems modelled by general probabilistic theories can be entangled.
Guillaume Aubrun (Institut Camille Jordan, Lyon)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
19:: Vladimir Kazakov - Matrix Model for Structure Constants of "Huge" Protected Operators in N=4 (...)
01.01.1970 · 01:00:00 ··· 10.06.2024 · 12:36:44 ··· ··· ··· ··· ··· ··· Huge operators in N = 4 SYM theory correspond to sources so heavy that they fully backreact on the space-time geometry. Here we study the protected correlation function of three such huge operators when they are given by 1/2 BPS operators , dual to IIB Strings in AdS5 × S 5 . We unveil simple matrix model representations for these correlators which we can sometimes solve analytically. For general huge operators, we transform this matrix model into a 1 + 1 dimensional integrable hydrodynamics problem. A discrete counterpart of this system -– the rational Calogero-Moser Model - helps to numerically solve the problem for general huge operators.
Vladimir Kazakov (Laboratoire de Physique de l'École Normale Supérieure, Paris)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
20:: Yevgeny Liokumovich - Width, scalar curvature and macroscopic scalar curvature
01.01.1970 · 01:00:00 ··· 03.06.2024 · 16:03:10 ··· ··· ··· ··· ··· ··· Gromov observed a surprising interplay between positive scalar curvature and a simple condition on the volumes of balls of fixed radius known as positive macroscopic scalar curvature. I will talk about some results about Urysohn width and lengths of closed geodesics in PSC and PMSC spaces, and how ideas travel back and forth between these two worlds.
Yevgeny Liokumovich (Toronto)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
21:: Alexey Balitsky - Waists measured via Urysohn width
01.01.1970 · 01:00:00 ··· 03.06.2024 · 16:02:49 ··· ··· ··· ··· ··· ··· The Urysohn width measures the "approximate dimension" of a riemannian manifold by approximating it with a lower-dimensional simplicial complex. Positive scalar curvature conjecturally implies upper bounds on the width. An inductive approach to this conjecture and related ones requires understanding of the following question: If our manifold is sliced into chunks of small approximate dimension, does that imply that the manifold itself has controlled approximate dimension? I will explain a few results in that direction, mostly of negative nature.
Alexey Balitsky (Luxembourg)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
22:: Nelia Charalambous - On the $L^p$ spectrum
01.01.1970 · 01:00:00 ··· 28.05.2024 · 14:38:32 ··· ··· ··· ··· ··· ··· In this talk, we will show that the resolvent set of the Laplacian on $L^p$ integrable $k$-forms lies outside a parabola whenever the volume of the manifold has an exponential volume growth rate, removing the requirement on the manifold to be of bounded geometry. Moreover, we find sufficient conditions on an open Riemannian manifold so that a Weyl criterion holds for the $L^p$-spectrum of the Laplacian on $k$-forms, and we provide a detailed description of the $L^p$ spectrum of the Laplacian on $k$-forms over hyperbolic space. The above results are joint work with Zhiqin Lu. We will also see a recent result with Julie Rowlett for the $L^p$ spectrum of conformally compact manifolds.
Nelia Charalambous (University of Cyprus)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
23:: Nadine Große - On spectra of Laplace and Dirac operators on noncompact manifolds
01.01.1970 · 01:00:00 ··· 28.05.2024 · 14:38:11 ··· ··· ··· ··· ··· ··· In this talk we give an overview over results on the spectrum of Laplace and Dirac operators on complete manifolds. After a general introduction to the different types of spectra, we review several results on spectra for special behaviors of the manifolds at infinity. At the end, we also discuss the influence of some additional potentials.
Nadine Große (Albert-Ludwigs-Universität Freiburg)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
24:: Julia Kempe - Synthetic Data – Friend or Foe in the Age of Scaling?
01.01.1970 · 01:00:00 ··· 26.05.2024 · 18:32:29 ··· ··· ··· ··· ··· ··· As AI and LLM model size grows, neural scaling laws have become a crucial tool to predict the improvements of large models when increasing capacity and the size of original (human or natural) training data. Yet, the widespread use of popular models means that the ecosystem of online data and text will co-evolve to progressively contain increased amounts of synthesized data.
In this talk we ask: How will the scaling laws change in the inevitable regime where synthetic data makes its way into the training corpus? Will future models, still improve, or be doomed to degenerate up to total (model) collapse? We develop a theoretical framework of model collapse through the lens of scaling laws. We discover a wide range of decay phenomena, analyzing loss of scaling, shifted scaling with number of generations, the ''un-learning" of skills, and grokking when mixing human and synthesized data. Our theory is validated by large-scale experiments with a transformer on an arithmetic task and text generation using the LLM Llama2.
Julia Kempe (NYU Center for Data Science and Courant Institute of Mathematical Sciences)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
25:: Gabriel Synnaeve - Grounding LLMs in Execution
01.01.1970 · 01:00:00 ··· 26.05.2024 · 12:16:50 ··· ··· ··· ··· ··· ··· Large language models (LLMs) are trained in a very simple way. Lots of properties we assign to them are already present in the training data. In this talk we will review how LLMs are trained today, what are new training paradigms that are aiming at grounding those LLMs in the impact of those generations. In the context of code generation, this is for instance groudning the LLM with the feedback of executing its generated code. For Lean proofstep prediction we can use tactics execution feedback similarly. We believe closing the loop between “open” generation and “grouding” with more formal system can bridge the gap between informal and formal LLM usages.
Gabriel Synnaeve (Meta AI Research)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
26:: Andrew Dudzik - Three Problems in the Mathematics of Deep Learning
01.01.1970 · 01:00:00 ··· 26.05.2024 · 12:16:21 ··· ··· ··· ··· ··· ··· Neural networks, particularly LLMs, are notoriously poor at algorithmic tasks, such as sorting, shortest path, and even basic arithmetic. Across three papers, we explored the problem of "aligning" architectures to classical computer programs, and showed that this question relates to familiar mathematical concepts: polynomial functors, cohomology, and higher categories.
Andrew Dudzik (Google DeepMind)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
27:: Francois Charton - Mathematics as a Translation Task - the Importance of Training Distributions
01.01.1970 · 01:00:00 ··· 26.05.2024 · 12:15:59 ··· ··· ··· ··· ··· ··· Many problems of mathematics can be set as translation tasks: problems, represented as sentences in some language, are translated into their solutions, by language models trained from synthetic examples. In this setting, we can choose the distribution of problems and solutions we use to train the model. I present examples from three different experiments, which suggest that this can make a large difference in model performance, and provide intuition on the inner workings of transformer models.
Francois Charton (Meta AI Research)
===
Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
28:: Yiannis Vlassopoulos - A First Approximation to the Mathematical Structure Computed by LLMs
01.01.1970 · 01:00:00 ··· 26.05.2024 · 12:15:36 ··· ··· ··· ··· ··· ··· Large Language Models are transformer neural networks which are trained to produce a probability distribution on the possible next words to given texts in a corpus, in such a way that the most likely word predicted, is the actual word in the training text.
We will explain what is the mathematical structure defined by such conditional probability distributions of text extensions. Changing the viewpoint from probabilities to -log probabilities we observe that the data of text extensions are encoded in a directed (non-symmetric) metric structure defined on the space of texts ${\mathcal L}$. We then construct a directed metric polyhedron $P({\mathcal L})$, in which ${\mathcal L}$ is isometrically embedded as generators of certain special extremal rays. Each such generator encodes extensions of a text along with the corresponding probabilities.
Moreover $P({\mathcal L})$ is $(\min, +)$ (i.e. tropically) generated by the text extremal rays and is the image of a $(\min,+)$ projector (given by the metric on ${\mathcal L}$). This leads to a duality theorem relating the polyhedron $P({\mathcal L})$ defined by text extensions to one defined by text restrictions. We also explain that the generator of the extremal ray corresponding to a text is approximated by a Boltzmann weighted linear combination of generators of extremal rays corresponding to the words making up that text.
The metric space ${\mathcal L}$ can equivalently be considered as an enriched category and then the embedding into $P({\mathcal L})$ is the Yoneda embedding into the category of presheaves. In fact all constructions have categorical meaning (in particular generalizing the familiar view of language as a monoid or as a poset with the subtext order). The categorical interpretations will be explained in parallel.
This is joint work with Stéphane Gaubert.
Yiannis Vlassopoulos (Athena Research Center)
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Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
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29:: Amaury Hayat - How can Machine Learning Help Mathematicians
01.01.1970 · 01:00:00 ··· 26.05.2024 · 12:15:05 ··· ··· ··· ··· ··· ··· Large Language models have known large successes in recent years. This naturally raises the question: can AI assist mathematicians in solving open problems in mathematics? We will explore how a language model can be trained to learn a mathematical intuition on open problems and guess candidate solutions, with a focus on a few examples. We will also explore the application of LLM to automated theorem proving with an online training procedure and discuss new perspectives in the area.
Amaury Hayat (École des Ponts ParisTech & CERMICS)
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Find this and many more scientific videos on https://www.carmin.tv/ - a French video platform for mathematics and their interactions with other sciences offering extra functionalities tailored to meet the needs of the research community.
===
30:: Albert Schwarz - 4/4 Quantum Mechanics and Quantum Field Theory from Algebraic and Geometric (...)
01.01.1970 · 01:00:00 ··· 15.05.2024 · 08:55:55 ··· ··· ··· ··· ··· ··· The course is based on a minibook that will be published by Springer. The text below is a shortened preface to this book.
In the conventional exposition of quantum mechanics, we work in Hilbert space and examine operators within this space. Self-adjoint operators are associated with physical quantities. Physicists predominantly use this methodology, however, it has its limitations. In this course we explore alternative viewpoints; our exposition does not depend on standard textbooks. We consider the algebraic approach, where the initial point is an algebra of observables, an associative algebra with involution, in which the self-adjoint elements are observables. This approach is nearly as old as quantum mechanics itself. In addition, we discuss the geometric approach, where the initial point is a set of states. This viewpoint was advocated in my recent papers; it is much more general. We demonstrate within the framework of this approach that quantum mechanics can be viewed as classical mechanics where our devices permit us to observe only a subset of physical quantities. Furthermore, we show that using this approach we can construct a wide class of physical theories that generalize quantum mechanics.
We highlight that the emergence of probabilities in quantum theory can be derived from decoherence caused by adiabatic interaction with a random environment. We underscore that the concept of a particle is not primary in quantum theory. If the theory is translation-invariant we define particles as elementary excitations of the ground state. Quasiparticles are elementary excitations of any translation-invariant state. We analyze the concept of scattering but we do not utilize the concept of a field and do not assume locality and Poincare invariance. We discuss not only the conventional scattering matrix (related to scattering cross-sections) but also the concept of an inclusive scattering matrix, which is closely related to the concept of inclusive scattering cross-sections. Scattering matrix can be expressed in terms of Green's functions by the well-known formula belonging to Lehmann, Symanczyk, and Zimmermann, and the inclusive scattering matrix can be expressed in terms of generalized Green's functions, which first appeared in nonequilibrium statistical physics in Keldysh formalism. As a concrete realization of the geometric approach, we describe the formalism of L-functionals where states are represented by non-linear functionals corresponding to positive functionals on Weyl and Clifford algebras (to states in the algebraic approach). L-functionals can be applied to solve the infrared problem in quantum electrodynamics.
Slides in pdf: https://download.carmin.tv/document/2414
Albert Schwarz (University of California at Davis)
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===
31:: Giuseppe Martone - Orbit Counting Theorem for Cusped Hitchin Representations
01.01.1970 · 01:00:00 ··· 23.06.2023 · 19:51:45 ··· ··· ··· ··· ··· ··· The dynamics of a cusped Hitchin representation can be encoded by a locally Holder continuous, eventually positive, non-arithmetic potential with an entropy gap at infinity on a topologically mixing countable Markov shift with the BIP property. After introducing and motivating these notions, I will present an orbit counting theorem for this class of shifts and potentials that, in turn, gives an orbit counting theorem for cusped Hitchin representations. This is joint work with Harry Bray, Dick Canary, and Nyima Kao
Giuseppe Martone (Yale University)
32:: François Labourie - Ghost Polygons, Poisson Bracket and Convexity
01.01.1970 · 01:00:00 ··· 23.06.2023 · 19:51:21 ··· ··· ··· ··· ··· ··· The moduli space of Anosov representations of a surface group in a group $\mathsf G$, which is an open set in the character variety, admits many more natural functions than the regular functions: length functions, correlation functions. We compute the Poisson bracket of those functions using some combinatorial device, show that the set of those functions is stable under the Poisson bracket and give an application to the convexity of length functions, generalizing the result of Kerckhoff on Teichmüller space.
We shall start by giving an introduction to Anosov representations, define precisely what are the functions we consider and explain the combinatorial device involved.
This is a joint work with Martin Bridgeman.
François Labourie (Université Côte d'Azur)
33:: Leon Carvajales - Thurston's Asymmetric Metrics for Anosov Representations
01.01.1970 · 01:00:00 ··· 23.06.2023 · 19:49:16 ··· ··· ··· ··· ··· ··· The Thurston metric is an asymmetric distance on the Teichmüller space of a surface, which is computed by comparing the lengths of closed curves in the two hyperbolic structures. Thurston introduced this metric and proved many interesting properties of it, which we will briefly summarize.
The theory of Anosov representations aims to generalize several aspects of the classical Teichmüller-Thurston theory to higher rank representations of hyperbolic groups. For instance, Bridgeman-Canary-Labourie-Sambarino applied the Thermodynamical Formalism to the underlying geodesic flow to construct pressure metrics on some spaces of Anosov representations, which generalize the Weil-Petersson metric on Teichmüller space. In this talk we will apply similar techniques to show that Thurston's asymmetric distance also generalizes to this setting. This is joint work with Xian Dai, Beatrice Pozzetti and Anna Wienhard.
Leon Carvajales (Universidad de la Republica, Montevideo)
34:: Andrés Sambarino - 2/2 Dynamics Associated to Anosov Representations: Some Geometric Consequences
01.01.1970 · 01:00:00 ··· 23.06.2023 · 17:19:33 ··· ··· ··· ··· ··· ··· We will review some dynamical systems associated to an Anosov representation and draw some geometric conclusions.
More precisely, we will review topics such as the Patterson-Sullivan Theory for these representations, the critical hypersurface, dynamical intersection, dynamics of the \theta-Weyl-chamber flow, and finally directional-conicality and generalizations.
We will then consider the approach of dominated sequences and draw conclusions on the regularity of limit sets.
Some relevant references are
lecture 1: Babillot-Ledrappier, Bridgeman-Canary-Labourie-S., Burger-Landesberg-Lee-Oh, Carvajales, Chow-Sarkar, Dey-Kapovich, Ledrappier, Lee-Oh, S.
lecture 2: Bochi-Potrie-S., Pozzetti-S., Pozzetti-S.-Wienhard, Zhang-Zimmer.
Andrés Sambarino (CNRS & IMJ-PRG)
35:: Andrew Zimmer - Transverse Groups
01.01.1970 · 01:00:00 ··· 23.06.2023 · 17:18:47 ··· ··· ··· ··· ··· ··· In this talk, I will discuss transverse groups (also called antipodal regular groups), a discrete group class containing the Anosov and relatively Anosov ones. I will describe a metric and flow space such a group acts on, which are analogous to the Cayley graph and the geodesic flow space of a word hyperbolic group. Then I will discuss how to use these spaces to prove new results. This represents joint work with Richard Canary and Tengren Zhang.
Andrew Zimmer (University of Wisconsin, Madison)
36:: Minju Lee - 2/2 Horospherically Invariant Measures and a Rank Dichotomy for Anosov Groups
01.01.1970 · 01:00:00 ··· 22.06.2023 · 16:56:51 ··· ··· ··· ··· ··· ··· Let $G$ be a product of simple real algebraic groups of rank one and $\Gamma$ be a Zariski dense and Anosov subgroup with respect to a minimal parabolic subgroup $P$. Let $N$ be the unipotent radical of $P$. For each direction $u$ in the interior of Weyl chamber, we show that there exists at most one $N$-invariant measure in $\Gamma\backslash G$ which is supported on the forward recurrent subset for the $\exp(tu)$-action. This can be viewed as a generalization of the unique ergodicity result for the horospherical action due to Furstenberg, Burger, Roblin and Winter for $\Gamma$ convex cocompact. This is joint work with Or Landesberg, Elon Lindenstrauss and Hee Oh.
Minju Lee (University of CHICAGO)
37:: Rafael Potrie - Homogeneous Dynamics and u-Gibbs States
01.01.1970 · 01:00:00 ··· 22.06.2023 · 16:53:31 ··· ··· ··· ··· ··· ··· Orbit closure and measure classification results are quite
central results and tools in homogeneous dynamics. Recently, new
techniques provided more 'robust' approaches to this kind of results
and it makes sense to try to extend some results to the
non-homogeneous setting. I will try to explain what would be the
natural questions in the non-linear setting and report some progress
in this direction.
Rafael Potrie (Universidad de la Republica, Montevideo)
38:: Andrés Sambarino - 1/2 Dynamics Associated to Anosov Representations: Some Geometric Consequences
01.01.1970 · 01:00:00 ··· 22.06.2023 · 09:19:10 ··· ··· ··· ··· ··· ··· We will review some dynamical systems associated to an Anosov representation and draw some geometric conclusions.
More precisely, we will review topics such as the Patterson-Sullivan Theory for these representations, the critical hypersurface, dynamical intersection, dynamics of the \theta-Weyl-chamber flow, and finally directional-conicality and generalizations.
We will then consider the approach of dominated sequences and draw conclusions on the regularity of limit sets.
Some relevant references are
lecture 1: Babillot-Ledrappier, Bridgeman-Canary-Labourie-S., Burger-Landesberg-Lee-Oh, Carvajales, Chow-Sarkar, Dey-Kapovich, Ledrappier, Lee-Oh, S.
lecture 2: Bochi-Potrie-S., Pozzetti-S., Pozzetti-S.-Wienhard, Zhang-Zimmer.
Andrés Sambarino (CNRS & IMJ-PRG)
39:: Minju Lee - 1/2 Discrete Subgroups with Finite Bowen-Margulis-Sullivan Measure in Higher Rank
01.01.1970 · 01:00:00 ··· 22.06.2023 · 09:18:15 ··· ··· ··· ··· ··· ··· Let G be a connected semisimple real algebraic group and D be its Zariski dense discrete subgroup. We prove that if D\G admits any finite Bowen-Margulis-Sullivan measure, then D is virtually a product of higher rank lattices and discrete subgroups of rank one factors of G. This may be viewed as a measure-theoretic analogue of classification of convex cocompact actions by Kleiner-Leeb and Quint, which was conjectured by Corlette in 1994. This is joint work with Mikolaj Fraczyk. We will then discuss its application on the bottom of the L^2 spectrum, in joint work with Samuel Edwards, Mikolaj Fraczyk and Hee Oh.
Minju Lee (University of CHICAGO)
40:: Tengren Zhang - 3/3 Anosov Representations
01.01.1970 · 01:00:00 ··· 22.06.2023 · 09:16:51 ··· ··· ··· ··· ··· ··· This minicourse is an introduction to the theory of Anosov representations for non-experts. There will be three lectures in this minicourse. In the first lecture, we will discuss Anosov representations and their various characterizations. In the second lecture, we will discuss the construction of domains of discontinuity for Anosov representations, as well as their relationship with convex projective geometry. In the final lecture, we will discuss recent developments and possible research directions for Anosov representations.
Tengren Zhang (National University of Singapore)
41:: Sam Edwards - The Bottom of the $L^2$ Spectrum of Higher-rank Locally Symmetric Spaces
01.01.1970 · 01:00:00 ··· 21.06.2023 · 15:50:34 ··· ··· ··· ··· ··· ··· For a rank one geometrically finite locally symmetric space Γ\X, the bottom of the $L^2$ spectrum of the Laplace operator is a simple eigenvalue corresponding to a positive eigenfunction if and only if the critical exponent of Γ is strictly greater than half the volume entropy of X. In particular, there exist infinite volume rank one locally symmetric spaces with square integrable positive Laplace eigenfunctions. In contrast, a higher-rank symmetric space Γ\X without rank one factors has a square integrable positive Laplace eigenfunction if and only Γ is a lattice. We will explain some aspects of the connection between square integrability of positive Laplace eigenfunctions and Patterson-Sullivan and Bowen-Margulis-Sullivan measures in the higher-rank setting. Based on joint work with Oh and Fraczyk-Lee-Oh.
Sam Edwards (Durham University)
42:: Sara Maloni - Geometric Structures Associated to Anosov Representations
01.01.1970 · 01:00:00 ··· 21.06.2023 · 15:50:11 ··· ··· ··· ··· ··· ··· Anosov representations can be considered a generalization of convex-cocompact representations to groups of higher-rank. In this talk, we are considering connected components of Anosov representations from the fundamental group of a closed hyperbolic manifold N, and which contains Fuchsian representations, and their associated domains of discontinuity. We will prove that the quotient of these domains of discontinuity is always smooth fiber bundles over N. Determining the topology of the fiber is hard in general, but we are able to describe it for representations in Sp(4,C), and for the domain of discontinuity in the space of complex Lagrangians in C^4 by using the classification of smooth 4-manifolds. This is joint work with Daniele Alessandrini, Nicolas Tholozan, and Anna Wienhard.
Sara Maloni (University of Virginia)
43:: Pratyush Sarkar - Local Mixing of Diagonal Flows on Anosov Homogeneous Spaces
01.01.1970 · 01:00:00 ··· 21.06.2023 · 15:49:43 ··· ··· ··· ··· ··· ··· For convex cocompact (and more generally, geometrically finite) rank one locally symmetric spaces, Winter proved mixing of the frame flow with respect to the Bowen-Margulis-Sullivan measure. Mixing results in homogeneous dynamics have many applications in counting, equidistribution, and decay of matrix coefficients. For Anosov subgroups of higher rank Lie groups, the analogous Bowen-Margulis-Sullivan measures are infinite and one looks for local mixing. In a joint work with Michael Chow, we prove local mixing of one-parameter diagonal flows on Anosov homogeneous spaces, generalizing the result of Winter. We also discuss some applications including a recent result of Chow-Fromm regarding joint equidistribution of maximal flat cylinders and holonomies.
Pratyush Sarkar (UC San Diego)
44:: Tengren Zhang - 2/3 Anosov Representations
01.01.1970 · 01:00:00 ··· 20.06.2023 · 19:59:20 ··· ··· ··· ··· ··· ··· This minicourse is an introduction to the theory of Anosov representations for non-experts. There will be three lectures in this minicourse. In the first lecture, we will discuss Anosov representations and their various characterizations. In the second lecture, we will discuss the construction of domains of discontinuity for Anosov representations, as well as their relationship with convex projective geometry. In the final lecture, we will discuss recent developments and possible research directions for Anosov representations.
Tengren Zhang (National University of Singapore)
45:: Jean-François Quint - 3/3 An Introduction to Geometry and Dynamics on Semisimple Lie Groups and (..)
01.01.1970 · 01:00:00 ··· 20.06.2023 · 19:59:04 ··· ··· ··· ··· ··· ··· The purpose of these lectures is to introduce certain objects and structure results on semisimple Lie groups, their structure theory, their discrete subgroups and the asymptotic behaviour of the latter.
Jean-François Quint (CNRS & Univ. Bordeaux)
46:: Marco Serone - 2/3 Resurgence in Integrable Field Theories
01.01.1970 · 01:00:00 ··· 12.04.2023 · 20:57:46 ··· ··· ··· ··· ··· ···
47:: Marco Serone - 1/3 Resurgence in Integrable Field Theories
01.01.1970 · 01:00:00 ··· 07.04.2023 · 15:04:50 ··· ··· ··· ··· ··· ···
48:: Pause mathématique
01.01.1970 · 01:00:00 ··· 06.04.2023 · 12:19:21 ··· ··· ··· ··· ··· ···
49:: Yakov Eliashberg - Interplay between notions of convexity in complex, symplectic and contact (...)
01.01.1970 · 01:00:00 ··· 28.03.2023 · 18:42:41 ··· ··· ··· ··· ··· ···
50:: Kai Cieliebak - Stein and Weinstein manifolds
01.01.1970 · 01:00:00 ··· 28.03.2023 · 18:42:09 ··· ··· ··· ··· ··· ···
51:: Jacques-Deric Rouault - Les Sept Filles d’Eve
01.01.1970 · 01:00:00 ··· 24.03.2023 · 17:00:10 ··· ··· ··· ··· ··· ···
52:: Sylvia Serfaty - 4/4 Systems with Coulomb Interactions: Mean-Field Limits and Statistical (...)
01.01.1970 · 01:00:00 ··· 22.03.2023 · 10:45:14 ··· ··· ··· ··· ··· ···
53:: Sylvia Serfaty - 3/4 Systems with Coulomb Interactions : Mean-Field Limits and Statistical (...)
01.01.1970 · 01:00:00 ··· 20.03.2023 · 23:29:37 ··· ··· ··· ··· ··· ···
54:: Sylvia Serfaty - 2/4 Systems with Coulomb Interactions: Mean-Field Limits and Statistical (...)
01.01.1970 · 01:00:00 ··· 18.03.2023 · 09:15:50 ··· ··· ··· ··· ··· ···
55:: Sylvia Serfaty - 1/4 Systems with Coulomb Interactions: Mean-Field Limits and Statistical (...)
01.01.1970 · 01:00:00 ··· 16.03.2023 · 22:27:34 ··· ··· ··· ··· ··· ···
56:: Antoine Cornuejols - Transfer Learning, Covariant Learning and Parallel Transport
01.01.1970 · 01:00:00 ··· 12.03.2023 · 14:21:36 ··· ··· ··· ··· ··· ···
57:: Nabil El Korso - Covariance & Subspace Inference: Handling Robustness, Variability and (...)
01.01.1970 · 01:00:00 ··· 12.03.2023 · 14:21:08 ··· ··· ··· ··· ··· ···
58:: Mathilde Mougeot - Leveraging Knowledge to Design Machine Learning Despite the Lack of (...)
01.01.1970 · 01:00:00 ··· 12.03.2023 · 14:20:26 ··· ··· ··· ··· ··· ···
59:: Aymeric Dieuleveut - Federated Learning with Communication Constraints: Challenges in (...)
01.01.1970 · 01:00:00 ··· 12.03.2023 · 14:19:46 ··· ··· ··· ··· ··· ···
60:: Isabelle Bloch - Hybrid AI for Knowledge Representation and Model-based Image Understanding - (...)
01.01.1970 · 01:00:00 ··· 12.03.2023 · 14:19:11 ··· ··· ··· ··· ··· ···
61:: Liam Mazurowski - Recent developments in constant mean curvature hypersurfaces II
01.01.1970 · 01:00:00 ··· 21.02.2023 · 13:48:53 ··· ··· ··· ··· ··· ···
62:: Xin Zhou - Recent developments in constant mean curvature hypersurfaces I
01.01.1970 · 01:00:00 ··· 21.02.2023 · 13:48:23 ··· ··· ··· ··· ··· ···
63:: Christina Sormani - Currents on metric spaces and intrinsic flat convergence
01.01.1970 · 01:00:00 ··· 11.02.2023 · 08:29:09 ··· ··· ··· ··· ··· ···
64:: Antoine Song - Spherical Plateau problem and applications
01.01.1970 · 01:00:00 ··· 11.02.2023 · 08:28:49 ··· ··· ··· ··· ··· ···
65:: Manjul BHARGAVA - Poetry, Drumming and Mathematics
01.01.1970 · 01:00:00 ··· 07.02.2023 · 10:33:46 ··· ··· ··· ··· ··· ···
66:: Robert Young - Self-similar solutions to extension and approximation problem
01.01.1970 · 01:00:00 ··· 30.12.2022 · 17:28:54 ··· ··· ··· ··· ··· ···
67:: Larry Guth - Lipschitz constant and degree of mappings
01.01.1970 · 01:00:00 ··· 30.12.2022 · 17:28:20 ··· ··· ··· ··· ··· ···
68:: Meilleurs vœux 2023 de l'IHES / Season's Greetings from IHES
01.01.1970 · 01:00:00 ··· 21.12.2022 · 09:13:32 ··· ··· ··· ··· ··· ···
69:: Yilin Wang - 4/4 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
01.01.1970 · 01:00:00 ··· 09.12.2022 · 12:10:54 ··· ··· ··· ··· ··· ···
70:: Yilin Wang - 3/3 The Loewner Energy at the Crossroad of Random Conformal Geometry (...)
01.01.1970 · 01:00:00 ··· 07.12.2022 · 20:22:39 ··· ··· ··· ··· ··· ···
71:: Alain Connes - Fonctions sphéroïdales et triplets spectraux
01.01.1970 · 01:00:00 ··· 07.12.2022 · 12:32:46 ··· ··· ··· ··· ··· ···
72:: Zhenguo Wei - Schatten Properties for Noncommutative Martingale Paraproduct
01.01.1970 · 01:00:00 ··· 04.12.2022 · 10:28:55 ··· ··· ··· ··· ··· ···
73:: Clément Dell’aiera - Paires de Hecke et K-théorie
01.01.1970 · 01:00:00 ··· 04.12.2022 · 10:28:25 ··· ··· ··· ··· ··· ···
74:: Kai Zeng - Schatten Properties of Commutators
01.01.1970 · 01:00:00 ··· 04.12.2022 · 10:28:02 ··· ··· ··· ··· ··· ···
75:: Paul Meunier - Quantum Automorphism Groups of Some Classes of Graphs
01.01.1970 · 01:00:00 ··· 04.12.2022 · 10:27:35 ··· ··· ··· ··· ··· ···
76:: Simon Townsend - Language Origins: an Animal Communication Perspective
01.01.1970 · 01:00:00 ··· 04.08.2022 · 13:28:24 ··· ··· ··· ··· ··· ···
77:: Shiing-Shen Chern - If Possible Do Nothing
01.01.1970 · 01:00:00 ··· 01.08.2022 · 12:57:15 ··· ··· ··· ··· ··· ···
78:: Michael Harris - 3/3 Derived Aspects of the Langlands Program
01.01.1970 · 01:00:00 ··· 29.07.2022 · 17:34:42 ··· ··· ··· ··· ··· ···
79:: Yiannis Sakellaridis - 2/2 Local and Global Questions “Beyond Endoscopy”
01.01.1970 · 01:00:00 ··· 29.07.2022 · 15:45:51 ··· ··· ··· ··· ··· ···
80:: Michael Harris, Tony Feng - 2/3 Derived Aspects of the Langlands Program
01.01.1970 · 01:00:00 ··· 29.07.2022 · 15:41:55 ··· ··· ··· ··· ··· ···
81:: Wei Zhang - 2/2 High-dimensional Gross–Zagier Formula
01.01.1970 · 01:00:00 ··· 29.07.2022 · 15:39:50 ··· ··· ··· ··· ··· ···
82:: Interview with Jessica Fintzen (University of Bonn)
01.01.1970 · 01:00:00 ··· 29.07.2022 · 09:22:30 ··· ··· ··· ··· ··· ···
83:: Yiannis Sakellaridis - 1/2 Local and Global Questions “Beyond Endoscopy”
01.01.1970 · 01:00:00 ··· 29.07.2022 · 09:20:08 ··· ··· ··· ··· ··· ···
84:: Tony Feng - 1/3 Derived Aspects of the Langlands Program
01.01.1970 · 01:00:00 ··· 29.07.2022 · 09:19:09 ··· ··· ··· ··· ··· ···
85:: David Ben-Zvi - Between Coherent and Constructible Local Langlands Correspondences
01.01.1970 · 01:00:00 ··· 28.07.2022 · 15:40:45 ··· ··· ··· ··· ··· ···
86:: Wei Zhang - 1/2 High-dimensional Gross–Zagier Formula
01.01.1970 · 01:00:00 ··· 28.07.2022 · 15:39:56 ··· ··· ··· ··· ··· ···
87:: Chao Li - 2/2 Geometric and Arithmetic Theta Correspondences
01.01.1970 · 01:00:00 ··· 28.07.2022 · 12:26:26 ··· ··· ··· ··· ··· ···
88:: Ana Caraiani - 3/3 Shimura Varieties and Modularity
01.01.1970 · 01:00:00 ··· 27.07.2022 · 19:04:18 ··· ··· ··· ··· ··· ···
89:: Chao Li - 1/2 Geometric and Arithmetic Theta Correspondences
01.01.1970 · 01:00:00 ··· 27.07.2022 · 12:12:46 ··· ··· ··· ··· ··· ···
90:: Ana Caraiani - 2/3 Shimura Varieties and Modularity
01.01.1970 · 01:00:00 ··· 27.07.2022 · 12:11:52 ··· ··· ··· ··· ··· ···