Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, February 24, 2015.

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Tuesday, February 24, 2015

11:00 am in 243 Altgeld Hall,Tuesday, February 24, 2015

Non-nilpotent elements in motivic homotopy theory

Michael Andrews   [email] (MIT)

Abstract: Classically, the nilpotence theorem of Devinatz, Hopkins, and Smith tells us that non-nilpotent self maps on finite p-local spectra induce nonzero homomorphisms on BP-homology. Motivically, over C, this theorem fails to hold: we have a motivic analog of BP and while $\eta:S^{1,1,}\to S^{0,0}$ induces zero on BP-homology, it is non-nilpotent. Work with Haynes Miller has led to a calculation of $\eta^{-1}\pi_{*,*}(S^{0,0})$, proving a conjecture of Guillou and Isaksen. Iíll introduce the motivic homotopy category and the motivic Adams-Novikov spectral sequence before describing this theorem. Then Iíll show that there are more periodicity operators in chromatic motivic homotopy theory than in the classical story. In particular, I will describe a new non-nilpotent self map.

1:00 pm in 347 Altgeld Hall,Tuesday, February 24, 2015

Nonlinear Phenomena in Acoustics: Traveling Waves, Bifurcations, and Singular Surfaces

Pedro Jordan (Naval Research Laboratory)

1:00 pm in 345 Altgeld Hall,Tuesday, February 24, 2015

Whitney's Extension Theorem in o-minimal structures

Athipat Thamrongthanyalak (Ohio State)

Abstract: For a $C^m$-function $f : U \to \mathbb{R}$, a jet of order $m$ of $f$ is the collection, $(D^{\alpha}f)_{\alpha\in\mathbb{N}^n,|\alpha|\leq n}$ of derivatives of $f$. In 1934, H. Whitney asked how can we determine whether a collection of continuous functions on a closed subset of $\mathbb{R}^n$ is a jet of order $m$ of a $C^m$-function. Here, we discuss this problem in o-minimal context.

1:00 pm in 243 Altgeld Hall,Tuesday, February 24, 2015

Planes, Trains & Automorphisms

Mark Bell (University of Warwick)

Abstract: We will discuss a new approach using train tracks to solve the conjugacy problem in the automorphism group of a punctured plane. This solution relies on the action of the mapping class group on the space of measured laminations and has several connections to veering triangulations of fibred 3--manifolds. Unlike techniques in braid groups using Garside structures, not only is this algorithm is effective it also generalises to all higher genus surfaces.

3:00 pm in 241 Altgeld Hall,Tuesday, February 24, 2015

New results for efficient hypergraph covering with application to large prime gaps

Kevin Ford   [email] (UIUC Math)

Abstract: Very recently, the author together with Ben Green, Sergei Konyagin, James Maynard and Terence Tao improved the bounds on the largest gaps between consecutive prime numbers. An important ingredient in the proof is a new result on efficient covering of hypergraphs, which extends a well-known theorem of Pippenger and Spencer from 1989. The Pippenger-Spencer theorem ensures the existence of a near-perfect packing of a hypergraph $H=(V,E)$ under three basic assumptions on $H$: (a) uniformity - all hyperedges $e\in E$ have the same (bounded) cardinality $k$; (b) regularity - the degree of each vertex $v\in V$ is asymptotically the same; (c) small codegrees - for all distinct $v,w\in V$, there are "few" edges containing both $v$ and $w$. Our new theorem gives essentially the same conclusion (not necessarily a packing, but an efficient near-covering) with a substantial weakening of hypotheses (a) and (b), while retaining (c) and the main hypothesis.

3:00 pm in 243 Altgeld Hall,Tuesday, February 24, 2015

t-structures on elliptic fibrations

Jason Lo (UIUC Math)

Abstract: A t-structure is a way to organise objects in the derived category. In various problems involving stabilities, t-structures come up naturally. In this talk, I will describe the various t-structures that appear in the derived category of coherent sheaves on an elliptic fibration with a Fourier-Mukai partner, and explain how understanding these t-structures might lead to progress on various problems on elliptic fibrations.