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for events the day of Tuesday, April 25, 2017.

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Tuesday, April 25, 2017

11:00 am in 345 Altgeld Hall,Tuesday, April 25, 2017

The signature modulo 8 of a fiber bundle

Carmen Rovi (Indiana)

Abstract: In this talk we shall be concerned with the residues modulo 4 and modulo 8 of the signature of a 4k-dimensional geometric Poincare complex. I will explain the relation between the signature modulo 8 and two other invariants: the Brown-Kervaire invariant and the Arf invariant. In my thesis I applied the relation between these invariants to the study of the signature modulo 8 of a fiber bundle, showing in particular that the non-multiplicativity of the signature modulo 8 is detected by an Arf invariant. In 1973 Werner Meyer used group cohomology to show that a surface bundle has signature divisible by 4. I will discuss current work with David Benson, Caterina Campagnolo and Andrew Ranicki where we are using group cohomology and representation theory of finite groups to detect non-trivial signatures modulo 8 of surface bundles.​

1:00 pm in 347 Altgeld Hall,Tuesday, April 25, 2017

Strichartz estimates for linear wave equations with moving potentials

Gong Chen (U Chicago)

Abstract: We will discuss Strichartz estimates for linear wave equations with several moving potentials in $\mathbb{R}^{3}$ (a.k.a. charge transfer Hamiltonians) which appear naturally in the study of nonlinear multisoliton systems. We show that local decay estimates systematically imply Strichartz estimates. To study local decay estimates, we introduce novel reversed Strichartz estimates along slanted lines and energy comparison under Lorentz transformations. As applications, we will also discuss related scattering problems and a construction of multisoliton in $\mathbb{R}^{3}$ with strong interactions.

1:00 pm in 345 Altgeld Hall,Tuesday, April 25, 2017

Differential-henselian extensions

Nigel Pynn-Coates (UIUC)

Abstract: The general motivating question is: What aspects of valuation theory can be adapted to the setting of valued differential fields, and under what assumptions? In valuation theory, henselian fields play an important role. I will concentrate on differential-henselian fields, introduced by Scanlon and developed in a more general setting by Aschenbrenner, van den Dries, and van der Hoeven. What do we know about uniqueness of differential-henselian extensions? Do differential-henselizations exist? After reviewing what is known, I will discuss my ongoing work towards answering these questions, and sketch a proof of the answers when the value group has finite archimedean rank. This talk is part of my preliminary examination.

2:00 pm in 347 Altgeld Hall,Tuesday, April 25, 2017

A new family of random sup-measures

Yizao Wang (University of Cincinnati)

Abstract: Random sup-measures are natural objects when investigating extremes of stochastic processes. A new family of stationary and self-similar random sup-measures are introduced. The representation of this family of random sup-measures is based on intersections of independent stable regenerative sets. These random sup-measures arise in limit theorems for extremes of a family of stationary infinitely-divisible processes with long-range dependence. The talk will first review random sup-measures in extremal limit theorems, and then focus on the representation of the new family of random sup-measures. Joint work with Gennady Samorodnitsky.

3:00 pm in Altgeld Hall,Tuesday, April 25, 2017

Small $k$-certificate in hypergraphs and representing all min-cuts

Chao Xu (Illinois Computer Science)

Abstract: For a hypergraph $H=(V,E)$, a hypergraph $H'=(V,E')$ is called a $k$-certificate of $H$ if it preserves all the cut values up to $k$. That is, $|\delta_{H'}(S)| \geq \min(|\delta_H(S)|,k)$ for all $S\subset V$. Nagamochi and Ibaraki showed there exists a $k$-certificate with $O(kn)$ edges for graphs, where $n$ is the number of vertices. A similar argument shows this extends to hypergraphs. We show a stronger result of hypergraphs: there is a $k$-certificate with size (sum of degrees) $O(kn)$, and it can be obtained by removing vertices from edges in $H$. We also devise an algorithm that finds a representation of all min-cuts in a hypergraph in the same running time as finding a single min-cut. The algorithm uses Cunningham's decomposition framework, and different generalizations of maximum adjacency ordering. This is joint work with Chandra Chekuri.

4:00 pm in 314 Altgeld Hall,Tuesday, April 25, 2017

Cobordisms: old and new

Ulrike Tillmann (Oxford University)

Abstract: Cobordims have played an important part in the classification of manifolds since their invention in the 1950s. In a different way, they are fundamental to the axiomatic approach to Topological Quantum Field Theory. In this colloquium style talk I will explain how recent results have shed new light on both of them.

The Tondeur Lectures in Mathematics will be held April 25-27, 2017. A reception will be held following the first lecture from 5-6 pm April 25 in 239 Altgeld Hall.