# Math Calendar

### Upcoming Events

## Methods of cyclic cohomology in index theory

Rudy Rodsphon, Vanderbilt University

Location: Stevenson 1310

The aim of this talk will be to review results in classical index theory through the point of view of cyclic cohomology, developed by Alain Connes as an alternative of de Rham homology in Noncommutative Geometry. We will then recall how it can be used to extend index theory beyond the classical setting. As an introduction to a second talk in two weeks, it will be elementary and accessible (I hope) to graduate students. In particular, it should not contain recent results.

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Jean Renault, Université d’Orléans

Location: Stevenson 1432

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Rudy Rodsphon, Vanderbilt University

Location: Stevenson 1310

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Zhengwei Liu, Harvard University

Location: Stevenson 1432

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Gili Golan, Vanderbilt University

Location: Stevenson 1310

## Combining Riesz bases in R^d

Shahaf Nitzen, Georgia Tech

Location: Stevenson 5211

Orthonormal bases (ONB) are used throughout mathematics and its applications. However, in many settings such bases are not easy to come by. For example, it is known that even the union of as few as two intervals may not admit an ONB of exponentials. In cases where there is no ONB, the next best option is a Riesz basis (i.e. the image of an ONB under a bounded invertible operator). In this talk I will discuss the following question: Does every finite union of rectangles in R^d, with edges parallel to the axes, admit a Riesz basis of exponentials? In particular, does every finite union of intervals in R admit such a basis? This is joint work with Gady Kozma. Tea at 3:30 pm in SC 1425. (Contact Person: Akram Aldroubi)

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Vlad Sergiescu, Université Joseph Fourier, Grenoble

Location: Stevenson 1432

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Brian Allen, University of Tennessee at Knoxville

Location: Stevenson 1307

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Yair Minsky, Yale

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Spencer Dowdall)

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Marcel Bischoff, Vanderbilt University

Location: Stevenson 1432

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Hugh Woodin, Harvard

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Vaughan Jones)

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Matthew Kennedy, University of Waterloo

Location: Stevenson 1432

## Mathematical Analysis of a Clonal Evolution Model of Tumour Cell Proliferation

Jozsef Farkas, University of Stirling (UK)

Location: Stevenson 1307

We introduce and analyse a partial differential equation model of a cancer cell population, which is structured with respect to age and telomere length of cells. We assume a continuous telomere length structure, which corresponds to the clonal model of tumour cell growth. This assumption leads to a model with a non-standard non-local boundary condition. We establish global existence of solutions and study their qualitative behaviour. In particular, we study the effect of telomere restoration on cancer cell dynamics. Our results indicate that without telomere restoration, the cell population typically dies out. On the other hand, with telomere restoration, we may observe exponential growth in the linear model. We also study the effects of crowding induced mortality on the qualitative behaviour, and study the existence and stability of steady states of a nonlinear model with crowding effect.

## On some problems of Cameron and Erdős

Jozsef Balogh, University of Illinois Urbana-Champaign

Location: Stevenson 5211

In 1990 and 1999, Cameron and Erdős proposed several problems in additive combinatorics. They asked about the number of sum-free sets, maximal sum-free sets, and Sidon sets in [n]={1,2, … n}. Additionally they asked for the number of sets in [n] containing no k-term arithmetic progression. In this talk we survey recent progress on these questions. One of the major tools in the proofs is the recently developed container lemma. The talk is based on joint results with Hong Liu, Robert Morris, Wojciech Samotij, Maryam Sharifzadeh and Andrew Treglown. Tea at 3:30 pm in SC 1425. (Contact Person: Victor Falgas-Ravry)

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Rolando de Santiago, University of Iowa

Location: Stevenson 1432

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Thomas Schlumprecht, Texas A&M

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Alex Powell)

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Christoph Walker, Leibniz Unversität Hannover (Germany)

Location: Stevenson 1307

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Daniel Hoff, UC San Diego

Location: Stevenson 1432

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Steve Shkoller, UC Davis

Location: Stevenson 5211

Tea at 3:30 pm in SC 1425. (Contact Person: Marcelo Disconzi)

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