09:15 AM  09:30 AM


Welcome

 Location
 SLMath: Eisenbud Auditorium
 Video


 Abstract
 
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09:30 AM  10:30 AM


Tensor valuations on lattice polytopes
Monika Ludwig (Technische Universität Wien)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Lattice polytopes are convex hulls of finitely many points with integer coordinates in ${\mathbb R}^n$. A function $Z$ from a family ${\cal F}$ of subsets of ${\mathbb R}^n$ with values in an abelian group is a valuation if $$ Z(P)+Z(Q)=Z(P\cup Q)+Z(P\cap Q) $$ whenever $P,Q,P\cup Q,P\cap Q\in{\cal F}$ and $Z(\emptyset)=0$. The classification of realvalued invariant valuations on lattice polytopes by Betke \& Kneser is classical (and will be recalled). It establishes a characterization of the coefficients of the Ehrhart polynomial. Building on this, classification results are established for vector, matrix, and general tensor valuations on lattice polytopes. The most important tensor valuations are the discrete moment tensors of rank $r$, $$ L^r(P)=\frac1{r!}\sum_{x\in P\cap{\mathbb Z}^n}x^r, $$ where $x^r$ denotes the $r$fold symmetric tensor product of the integer point $x\in{\mathbb Z}^n$, and its coefficients in the Ehrhart tensor polynomial, called Ehrhart tensors. However, it is shown that there are additional examples for tensors of rank nine with the same covariance properties. For tensors of rank up to eight, a complete classification is established
 Supplements


10:30 AM  11:00 AM


Break

 Location
 SLMath: Atrium
 Video


 Abstract
 
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11:00 AM  12:00 PM


Concentration of measure on the orthogonal group and highdimensional geometry
Elizabeth Meckes (Case Western Reserve University)

 Location
 SLMath: Eisenbud Auditorium
 Video

 Abstract
Many important features of the geometry of highdimensional spaces can be seen as consequences of concentration of measure on the orthogonal group. I will illustrate this phenomenon with three examples: the JohnsonLindenstrauss lemma, Dvoretzky's theorem, and a measure theoretic analog of the latter. The talk will be elementary and assume no prior knowledge of measure concentration or any of the results to be discussed.
 Supplements


12:00 PM  02:00 PM


Lunch

 Location
 SLMath: Atrium
 Video


 Abstract
 
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02:00 PM  03:00 PM


Uniqueness of a smooth convex body with uniform cone volume measure in the neighborhood of a ball
Galyna Livshyts (Georgia Institute of Technology)

 Location
 
 Video

 Abstract
We prove that in every ndimensional there exists a constant c=c(n)>0 so that in the c(n)neighborhood of a ball, the only convex body with uniform cone volume measure is the ball. The goal of the talk will be to give an insight into some analytic aspects of the LogBrunnMinkowski and LogMinkowski conjectures made by Boroczky, Lutwak, Yang and Zhang. This talk is based on the joint papers with Colesanti, Marsiglietti and Colesanti.
 Supplements



03:00 PM  03:30 PM


Tea

 Location
 SLMath: Atrium
 Video


 Abstract
 
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03:30 PM  04:30 PM


Panel Discussion

 Location
 SLMath: Commons Room
 Video


 Abstract
 
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06:30 PM  08:30 PM


Dinner at the Taste of Himalayas

 Location
 Taste of Himlayas
 Video


 Abstract
 
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