Department of

Mathematics


Seminar Calendar
for events the day of Wednesday, September 10, 2014.

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Wednesday, September 10, 2014

12:00 pm in 141 Coordinated Science Laboratory,Wednesday, September 10, 2014

Adaptive and Scalable Sequential Detection Rules

Georgios Fellouris   [email] (UIUC Statistics)

Abstract: In this talk, I will discuss the problem of signal detection when observations are sequentially acquired from a large number of sources and the (unknown) subset of sources in which signal is present is small. I will propose a class of sequential detection rules that are characterized by adaptiveness, in the sense that they are asymptotically optimal under any scenario for the subset of affected sources, and scalability, in the sense that the operations required for the computation of the corresponding test statistic at any given time scales linearly with the number of sources.

2:00 pm in Altgeld Hall 441,Wednesday, September 10, 2014

What is $^{L}G$?

Brian Collier   [email] (UIUC Math)

Abstract: In this talk will define the Langlands dual of a reductive complex Lie group. Along the way root data and other important ideas from Lie theory will be introduced. No knowledge of Lie theory will be assumed beyond Linear algebra. We will NOT discuss what the geometric Langlands program is about, however, time permitting, one role of the Langlands dual in the theory of Higgs bundles will be mentioned.

3:00 pm in 347 Altgeld Hall,Wednesday, September 10, 2014

Dimers and arctic curves of the octahedron relation

Rodrigo Soto-Garrido (UIUC Physics)

Abstract: We study the T-system, also known as the octahedron relation, which solution corresponds to the partition function for dimer coverings of the Aztec Diamond graph. After studying the solutions for the uniform initial data, we find exact solutions for a particular (and more general) class of periodic initial conditions. We show that the density function, that measures average dimer occupation of a face of the Aztec graph, obeys a linear system of equations with periodic coefficients. We explore the thermodynamic limit of the dimer models and derive exact "arctic" curves (generalizing the arctic circle for domino tilings on the aztec diamond) separating various phases. We finish with a discussion of possible generalizations and future applications to other recursion relations (joint work with P. Di Francesco).

4:00 pm in 245 Altgeld Hall,Wednesday, September 10, 2014

Gaps between prime numbers

Kevin Ford (Department of Mathematics, University of Illinois at Urbana-Champaign)