# Math Calendar

### Upcoming Events

## Chvatal-Erdos Condition of Prism-Hamiltonicity

Pouria Salehi, Vanderbilt University

Location: Stevenson 1431

The prism over a graph G is the Cartesian product of G with the complete graph of order 2. If this product is Hamiltonian, we say that G is prism-Hamiltonian. In this talk we find sharp Chvatal-Erdos condition of G for the existence of a Hamiltonian cycle in the prism over G and the Cartesian product of G with the complete graph of order k. D. West asked the following question : Given a positive integer k, what is the largest value of a, such that if G has connectivity k and independence number a, then the prism over G is Hamiltonian?

There are sharp examples which show that such a must be between k and 2k. We show the sharp result, that for a k-connected graph G with independent number less than or equal to 2k, is prism-Hamiltonian. As a generalization of this result, for a graph G we proved result for Hamiltonicity of the Cartesian product of G with complete graph of order k.

## The Banach-Tarski Paradox

Gili Golan, Vanderbilt University

Location: SC 1206

The Banach-Tarski Paradox says that it is possible to cut a ball into 5 disjoint pieces and rearrange the pieces to get two balls of the same size. We would talk about the Axiom of Choice which implies the Banach-Tarski Paradox and discuss some Group Theory results which form the basis for the paradox.

## Algebraic Models of Homotopy Types

Angelica Osorno, Reed College

Location: Stevenson 1310

One of the goals of algebraic topology is to classify topological spaces up to homotopy. This task becomes more manageable when we restrict to spaces that only have finitely many non-vanishing homotopy groups. In this talk I will give a historical account of the different algebraic models that have been developed to classify finite homotopy types, with a special emphasis on recent joint work with N. Gurski, N. Johnson and Marc Stephan on modeling stable 2-types.

Contact Person: (Anna Marie Bohmann)

## Poisson Boundaries of Finite von Neumann Algebras

Sayan Das, Vanderbilt University

Location: SC 1310

In my talk, I shall discuss Izumi’s notion of noncommutative Poisson boundary, in the setting of finite von Neumann algebras. I shall also talk about a noncommutative generalization of Kaimanovich’s “Double Ergodicity of the boundary”, and provide some applications to the study bounded derivations on a finite von Neumann algebras. (Joint work with J. Peterson)

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Hayden Jansen, Vanderbilt University

Location: SC 1206

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Sahana Balasubramanya, Vanderbilt University

Location: SC 1308

## The 16th Hilbert Problem: Disclosed and Hidden.

Slava Kharlamov of Strasbourg University, France

Location: SC 5211

The talk will be focused on the first part of this problem: the part devoted by Hilbert to topological properties of real algebraic curves and surfaces. It is this part, together with 9 other problems of the famous list that was chosen by Hilbert for the oral presentation. In this talk we will present certain milestones achieved in the directions influenced by this problem. In particular, we will mention those which allowed to respond to at least those of Hilbert questions he posed precisely. We will try to explain at least some of the multitude of new ideas, methods and theories disclosed (giving preference to topological and geometrical settings), but also to list selected, still open, questions.

Tea at 3:30 pm in SC 1425. (Contact Person: Rares Rasdeaconu)

## Talk Title TBA

Radu Ionas, C.N. Yang Institute for Theoretical Physics, Stony Brook University

Location: SC 1310

## Lipschitz Properties of General Convolutional Neural Networks

Radu Balan, University of Maryland

Location: SC 5211

In this talk we give a general framework for convolutional neural networks (ConvNets) which covers most popular ConvNets in use. We prove that the Lipschitz bound of such a ConvNet can be determined by solving a linear program. Additionally we provide a simpler and more explicit expression for an upper bound. We use our framework to analyze some examples of ConvNets. This is a joint work with Dongmian Zou (UMD) and Maneesh Singh (Verisk).

Tea at 3:30 pm in SC 1425. (Contact Person: Akram Aldroubi)

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Scott Atkinson, Vanderbilt University

Location: SC 1310

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Oleg Bogopolski, Universität Düsseldorf

Location: SC 1308

## Paths of Minimal Lengths on the Set of Exact Differential 2–Forms.

Wilfrid Gangbo, UCLA

Location: Stevenson 5211

In this talk, we recall the definition of the group S of Hamiltonian symplectomorphisms on a contractible subset of a finite dimensional space. We first show that the L^2–projection onto S induces a metric on the set of exact differential 2–forms. We then show how all of these connect to what we term, the symplectic factorization of vector fields. We strive to characterize the geodesics of minimal length and the regularity properties of the projections onto S (this talk is based on joint work with B. Dacorogna and O. Kneuss).

Tea at 3:30 pm in SC 1425. (Contact Person: Gieri Simonett)

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Arman Darbinyan, Vanderbilt University

Location: SC 1308

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Matthieu Jacquemet, Vanderbilt University

Location: SC 1206

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Gennadi Kasparov, Vanderbilt University

Location: SC 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Bruce Hughes)

## Talk Title TBA

Mehdi Lejmi, CUNY Bronx Community College

Location: SC 1310

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