Aug 21, 2017
Monday
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09:00 AM - 09:10 AM
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Welcome
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- Location
- SLMath: Eisenbud Auditorium
- Video
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--
- Abstract
- --
- Supplements
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09:10 AM - 10:10 AM
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Geometry of isotropic convex bodies
Apostolos Giannopoulos (National and Kapodistrian University of Athens (University of Athens))
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
The aim of the talks will be to present the main results on the geometry of isotropic convex bodies in connection with a number of well-known open questions regarding the distribution of volume in high-dimensional convex bodies, such as the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture.
- Supplements
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10:10 AM - 11:00 AM
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Break - View the Eclipse
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
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--
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11:00 AM - 12:00 PM
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Deviations of random matrices and applications
Roman Vershynin (University of Michigan)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This series of lectures will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in geometric functional analysis and data science, in particular to covariance estimation, signal recovery, and sparse regression.
- Supplements
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--
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12:00 PM - 02:00 PM
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Lunch
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
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--
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02:00 PM - 03:00 PM
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Mixing in product spaces
Elchanan Mossel (Massachusetts Institute of Technology)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Mixing properties of dynamical systems are a central topic of study in mathematics.
In the lectures we will take a modern, probabilistic, short horizon quantitative view of this problem and see that it involves a number of areas in modern mathematics including isoperimetric theory, noise stability and additive combinatorics. We will explain where are we in a quest for a unified theory as well as some of the applications of this theory.
- Supplements
-
--
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03:00 PM - 03:30 PM
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Tea
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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03:30 PM - 04:30 PM
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Geometric classification
Monika Ludwig (Technische Universität Wien)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
A fundamental theorem of Hadwiger classifies all rigid-motion invariant and continuous functionals on convex bodies (that is, compact convex sets) in ${\mathbb R}^n$ that satisfy the inclusion-exclusion principle, $$\operatorname{Z}(K)+ \operatorname{Z}(L) =\operatorname{Z}(K\cup L) +\operatorname{Z}(K\cap L)$$ for convex bodies $K$ and $L$ such that $K\cup L$ is convex. Under weak additional assumptions, such a functional $\operatorname{Z}$ is a finitely additive measure and hence Hadwiger's theorem is a counterpart to the classification of Haar measures. Hadwiger's theorem characterizes the most important functionals within Euclidean geometry, the $n+1$ intrinsic volumes, which include volume, surface area, and the Euler characteristic. In recent years, numerous further functions and operators defined on the space of convex bodies and more generally on function spaces were characterized by their properties. An overview of these results will be given:\\ \hspace*{16pt}\parbox{16pt}{(i)} Real and tensor valuations\\ \hspace*{16pt}\parbox{16pt}{(ii)} Minkowski valuation\\ \hspace*{16pt}\parbox{16pt}{(iii)} Valuations on function spaces.\\ The focus is on valuations that intertwine the SL$(n)$ and on connections to geometric functional analysis and analytic inequalities.
- Supplements
-
--
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Aug 22, 2017
Tuesday
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09:30 AM - 10:30 AM
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Gaussian convexity
Ramon Van Handel (Princeton University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
It has long been known that Gaussian measures possess unique convexity properties within the class of log-concave measures. In particular, a remarkable sharp form of Gaussian convexity was discovered by A. Ehrhard in the early 1980s, but has mostly remained somewhat of a beautiful curiosity. In recent work, however, this inequality, the theory surrounding it, and its utility in applications have become significantly better understood. My aim in these talks is to review and discuss in some detail several recent developments surrounding this theory and its applications to Gaussian concentration phenomena (by us as well as by other authors). I will also highlight some key mysteries that remain.
- Supplements
-
--
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10:30 AM - 11:00 AM
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Break
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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11:00 AM - 12:00 PM
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Brunn-Minkowski theory, functionalization of geometric notions and inequalities 1. Volume inequalities
Shiri Artstein (Tel Aviv University)
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- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
We will discuss fundamentals of Brunn Minkowski theory via the functional versions of basic geometric notions and inequalities.
- Supplements
-
--
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12:00 PM - 02:00 PM
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Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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02:00 PM - 03:00 PM
|
|
Mixing in product spaces
Elchanan Mossel (Massachusetts Institute of Technology)
|
- Location
- SLMath: Atrium
- Video
-
- Abstract
Mixing properties of dynamical systems are a central topic of study in mathematics.
In the lectures we will take a modern, probabilistic, short horizon quantitative view of this problem and see that it involves a number of areas in modern
mathematics including isoperimetric theory, noise stability and additive combinatorics. We will explain where are we in a quest for a unified theory as well as some of the applications of this theory.
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Geometry of isotropic convex bodies
Apostolos Giannopoulos (National and Kapodistrian University of Athens (University of Athens))
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
The aim of the talks will be to present the main results on the geometry of isotropic convex bodies in connection with a number of well-known open questions regarding the distribution of volume in high-dimensional convex bodies, such as the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture.
- Supplements
-
Notes
869 KB application/pdf
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04:30 PM - 06:20 PM
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Reception
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- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
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Aug 23, 2017
Wednesday
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09:30 AM - 10:30 AM
|
|
Geometric classification
Monika Ludwig (Technische Universität Wien)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
A fundamental theorem of Hadwiger classifies all rigid-motion invariant and continuous functionals on convex bodies (that is, compact convex sets) in ${\mathbb R}^n$ that satisfy the inclusion-exclusion principle, $$\operatorname{Z}(K)+ \operatorname{Z}(L) =\operatorname{Z}(K\cup L) +\operatorname{Z}(K\cap L)$$ for convex bodies $K$ and $L$ such that $K\cup L$ is convex. Under weak additional assumptions, such a functional $\operatorname{Z}$ is a finitely additive measure and hence Hadwiger's theorem is a counterpart to the classification of Haar measures. Hadwiger's theorem characterizes the most important functionals within Euclidean geometry, the $n+1$ intrinsic volumes, which include volume, surface area, and the Euler characteristic. In recent years, numerous further functions and operators defined on the space of convex bodies and more generally on function spaces were characterized by their properties. An overview of these results will be given:\\ \hspace*{16pt}\parbox{16pt}{(i)} Real and tensor valuations\\ \hspace*{16pt}\parbox{16pt}{(ii)} Minkowski valuation\\ \hspace*{16pt}\parbox{16pt}{(iii)} Valuations on function spaces.\\ The focus is on valuations that intertwine the SL$(n)$ and on connections to geometric functional analysis and analytic inequalities.
- Supplements
-
--
|
10:30 AM - 11:00 AM
|
|
Break
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
Deviations of random matrices and applications
Roman Vershynin (University of Michigan)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This series of lectures will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in geometric functional analysis and data science, in particular to covariance estimation, signal recovery, and sparse regression.
- Supplements
-
--
|
|
Aug 24, 2017
Thursday
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09:30 AM - 10:30 AM
|
|
Mixing in product spaces
Elchanan Mossel (Massachusetts Institute of Technology)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Mixing properties of dynamical systems are a central topic of study in mathematics.
In the lectures we will take a modern, probabilistic, short horizon quantitative view of this problem and see that it involves a number of areas in modern
mathematics including isoperimetric theory, noise stability and additive combinatorics. We will explain where are we in a quest for a unified theory as well as some of the applications of this theory.
- Supplements
-
--
|
10:30 AM - 11:00 AM
|
|
Break
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
Geometry of isotropic convex bodies
Apostolos Giannopoulos (National and Kapodistrian University of Athens (University of Athens))
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
The aim of the talks will be to present the main results on the geometry of isotropic convex bodies in connection with a number of well-known open questions regarding the distribution of volume in high-dimensional convex bodies, such as the slicing problem, the thin shell conjecture and the Kannan-Lovász-Simonovits conjecture.
- Supplements
-
|
12:00 PM - 02:00 PM
|
|
Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
02:00 PM - 03:00 PM
|
|
Gaussian convexity
Ramon Van Handel (Princeton University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
It has long been known that Gaussian measures possess unique convexity properties within the class of log-concave measures. In particular, a remarkable sharp form of Gaussian convexity was discovered by A. Ehrhard in the early 1980s, but has mostly remained somewhat of a beautiful curiosity. In recent work, however, this inequality, the theory surrounding it, and its utility in applications have become significantly better understood. My aim in these talks is to review and discuss in some detail several recent developments surrounding this theory and its applications to Gaussian concentration phenomena (by us as well as by other authors). I will also highlight some key mysteries that remain.
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Brunn-Minkowski theory, functionalization of geometric notions and inequalities 2. Duality and Central symmetry
Shiri Artstein (Tel Aviv University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
We will discuss fundamentals of Brunn Minkowski theory via the functional versions of basic geometric notions and inequalities.
- Supplements
-
--
|
|
Aug 25, 2017
Friday
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09:30 AM - 10:30 AM
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Brunn-Minkowski theory, functionalization of geometric notions and inequalities 3. Covering numbers
Shiri Artstein (Tel Aviv University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
We will discuss fundamentals of Brunn Minkowski theory via the functional versions of basic geometric notions and inequalities.
- Supplements
-
--
|
10:30 AM - 11:00 AM
|
|
Break
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
11:00 AM - 12:00 PM
|
|
Deviations of random matrices and applications
Roman Vershynin (University of Michigan)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
Uniform laws of large numbers provide theoretical foundations for statistical learning theory. This series of lectures will focus on quantitative uniform laws of large numbers for random matrices. A range of illustrations will be given in geometric functional analysis and data science, in particular to covariance estimation, signal recovery, and sparse regression.
- Supplements
-
--
|
12:00 PM - 02:00 PM
|
|
Lunch
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
02:00 PM - 03:00 PM
|
|
Geometric classification
Monika Ludwig (Technische Universität Wien)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
A fundamental theorem of Hadwiger classifies all rigid-motion invariant and continuous functionals on convex bodies (that is, compact convex sets) in ${\mathbb R}^n$ that satisfy the inclusion-exclusion principle, $$\operatorname{Z}(K)+ \operatorname{Z}(L) =\operatorname{Z}(K\cup L) +\operatorname{Z}(K\cap L)$$ for convex bodies $K$ and $L$ such that $K\cup L$ is convex. Under weak additional assumptions, such a functional $\operatorname{Z}$ is a finitely additive measure and hence Hadwiger's theorem is a counterpart to the classification of Haar measures. Hadwiger's theorem characterizes the most important functionals within Euclidean geometry, the $n+1$ intrinsic volumes, which include volume, surface area, and the Euler characteristic. In recent years, numerous further functions and operators defined on the space of convex bodies and more generally on function spaces were characterized by their properties. An overview of these results will be given:\\ \hspace*{16pt}\parbox{16pt}{(i)} Real and tensor valuations\\ \hspace*{16pt}\parbox{16pt}{(ii)} Minkowski valuation\\ \hspace*{16pt}\parbox{16pt}{(iii)} Valuations on function spaces.\\ The focus is on valuations that intertwine the SL$(n)$ and on connections to geometric functional analysis and analytic inequalities
- Supplements
-
--
|
03:00 PM - 03:30 PM
|
|
Tea
|
- Location
- SLMath: Atrium
- Video
-
--
- Abstract
- --
- Supplements
-
--
|
03:30 PM - 04:30 PM
|
|
Gaussian convexity
Ramon Van Handel (Princeton University)
|
- Location
- SLMath: Eisenbud Auditorium
- Video
-
- Abstract
It has long been known that Gaussian measures possess unique convexity properties within the class of log-concave measures. In particular, a remarkable sharp form of Gaussian convexity was discovered by A. Ehrhard in the early 1980s, but has mostly remained somewhat of a beautiful curiosity. In recent work, however, this inequality, the theory surrounding it, and its utility in applications have become significantly better understood. My aim in these talks is to review and discuss in some detail several recent developments surrounding this theory and its applications to Gaussian concentration phenomena (by us as well as by other authors). I will also highlight some key mysteries that remain.
- Supplements
-
--
|
|