Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, September 13, 2016.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, September 13, 2016

11:00 am in 345 Altgeld Hall,Tuesday, September 13, 2016

An equivariant motivic slice filtration

Jeremiah Heller (Illinois Math)

Abstract: Mixing Voevodsky's filtration in motivic homotopy and Dugger's in C_2-equivariant homotopy theory leads to an interesting filtration on the C_2-equivariant motivic homotopy category. I'll talk about some joint work with P. A. Ostvaer, where we compute the resulting zero slice of the equivariant motivic sphere spectrum.

1:00 pm in 345 Altgeld Hall,Tuesday, September 13, 2016

No seminar this week

1:00 pm in 7 Illini Hall,Tuesday, September 13, 2016

Abelian von Neumann Algebras

Chris Gartland   [email] (UIUC Math)

Abstract: We will define the categories of abelian von Nuemann algebras, boolean algebras, stone spaces, and measurable spaces. We will sketch a construction of certain functors between these categories that, when restricted to the right subcategories, become equivalences or dualities. von Neumann algebras are often referred to as "noncommutative measure spaces" because of the duality in the abelian case.

2:00 pm in 241 Altgeld Hall ,Tuesday, September 13, 2016

Sieve methods and Fouvry-Iwaniec primes

Kyle Pratt   [email] (UIUC )

Abstract: Sieve methods were invented in order to find prime numbers in various sequences. In their original incarnation sieves are unfortunately incapable of fulfilling their intended purpose, due to a fundamental obstruction known as the "parity problem''. However, with additional analytic input it is sometimes possible to break the parity barrier and find primes in interesting sequences. In this talk, the first in a series of two lectures, we begin exploring the result of Fouvry and Iwaniec that there are infinitely many primes $p$ of the form $p = x^2+\ell^2$, where $\ell$ itself is a prime. We discuss the "sieve-theoretic'' aspects of the proof, and study an interesting spacing problem for rational points coming from roots of a quadratic congruence.

2:00 pm in 243 Altgeld Hall,Tuesday, September 13, 2016

Sums of Squares on projective varieties

Rainier Sinn (Georgia Tech)

Abstract: We will consider the question whether we can write every nonnegative quadratic form on a real projective variety as a sum of squares in its coordinate ring. In this talk, we will focus mostly on irreducible projective varieties and determine the minimal length of sum-of-squares representations on nice varieties. I will mention results from recent joint works with Greg Blekherman, Daniel Plaumann, and Cynthia Vinzant as well as Greg Blekherman and Mauricio Velasco.

3:00 pm in 241 Altgeld Hall,Tuesday, September 13, 2016

Online Sum Paintability: The Slow-Coloring Game

Douglas B. West (Zhejiang Normal University and University of Illinois)

Abstract: The "slow-coloring game" is played by Lister and Painter on a graph $G$. On each round, Lister marks a nonempty subset $M$ of the remaining vertices, scoring $|M|$ points. Painter then deletes a subset of $M$ that is independent in $G$. The game ends when all vertices are deleted. Painter's goal is to minimize the total score; Lister seeks to maximize it. The score that each player can guarantee doing no worse than is the "slow-color cost" of $G$, written $s(G)$. The game is a variant of online list coloring. We have obtained the following results. Trivially lower and upper bounds on $s(G)$ are the chromatic sum and the sum-paintability, with equality in the lower bound when $\alpha(G)\le2$ and equality in the upper bound if and only if all components are complete (the "chromatic sum" is the minimum sum of vertex colors in a proper coloring by positive integers). We give sharp upper and lower bounds on $s(G)$ in terms of the independence number. Among $n$-vertex trees, $s(G)$ is minimized by the star and maximized by the path (where it equals $3n/2$). We give good bounds on $s(K_{r,s})$. These results are joint with Thomas Mahoney and Gregory Puleo. We will also discuss a later linear-time algorithm to compute $s(G)$ exactly when $G$ is a tree, which is joint work with Gregory Puleo.

3:00 pm in 245 Altgeld Hall,Tuesday, September 13, 2016

Basic LGBTQ Ally Training

Abstract: In the Basic LGBTQ Ally Training workshop, you will learn about LGBT identities as well as current issues affecting these communities. You will also learn basic ally skills and how to implement these skills utilizing a decision making process. Workshop will be from 3:00-5:00 p.m., followed by a reception in 239 Altgeld Hall from 5-6 p.m. Everyone in the department is welcome and encouraged to attend.