Department of

Mathematics


Seminar Calendar
for events the day of Thursday, November 12, 2015.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Thursday, November 12, 2015

11:00 am in 241 Altgeld Hall,Thursday, November 12, 2015

Quotients of sums of distinct powers of three

Bruce Reznick (UIUC Math)

Abstract: Let $A$ denote the set of Newman polynomials, $\sum c_i x^i, c_i \in \{0,1\}$. Which integers $m$ may be written as $m = \frac{p(3)}{q(3)}$, where $p, q \in A$? There are two complementary approaches: the algebraic and the combinatorial. In the first, one can show that 4 arises only when $p(x) = (1+x)q(x)$ and if 22 arises, then $q$ cannot divide $p$. In the second, all possible $q$'s are encoded by certain labeled closed walks in an uncomplicated digraph; in this way it can be shown that 529 and 592 can never occur. No particular prerequisites for this seminar.

12:30 pm in 464 Loomis Laboratory,Thursday, November 12, 2015

Algebraic structures in superconformal field theories

Chris Beem (IAS)

Abstract: The bootstrap approach to conformal field theory adopts an algebraic framework based on the operator product expansion  to study strongly interacting CFTs. In general this algebraic structure is not analytically tractable. In contrast, in theories with  a sufficient amount of supersymmetry, there turn out to be operator subalgebras that are quite tractable. From these one may  determine a large amount of information about the spectrum of supersymmetric operators and their three point couplings. I will describe the situation for superconformal field theories in three, four, and six dimensions.

1:00 pm in Altgeld Hall 243,Thursday, November 12, 2015

Convergence of harmonic maps

Zahra Sinaei (Northwestern University)

Abstract: In this talk I will present a compactness theorem for a sequence of harmonic maps which are defined on a converging sequence of Riemannian manifolds. The sequence of manifolds will be considered in the space of compact n-dimensional Riemannian manifolds with bounded sectional curvature and bounded diameter, equipped with measured Gromov-Hausdorff topology.

2:00 pm in 347 Altgeld Hall,Thursday, November 12, 2015

Complete Segal Objects

Nima Rasekh   [email] (UIUC Math)

Abstract: In this talk we review some basics of higher category theory from the perspective of complete Segal spaces. Towards the end we introduce a mild generalization, complete Segal objects.

2:00 pm in 243 Altgeld Hall,Thursday, November 12, 2015

What should a quantum isometry be?

Alexandru Chirvasitu (University of Washington, Seattle)

Abstract: In the context of non-commutative geometry, "spaces" are modeled as C*-algebras thought of as possibly non-commutative algebras of continuous functions, and compact quantum groups are then C*-algebras with enough additional structure so that they behave in many ways like their commutative counterparts (i.e. algebras of continuous functions on compact groups). The notion of an action of a compact quantum group on a (possibly non-commutative) space is well established by now, but when the space in question is equipped with some additional structure, it is often unclear what it would mean for the quantum action to be structure-preserving. The talk is about actions of quantum groups on compact metric spaces. The main point will be that several competing notions of isometric action that coalesce in the classical case (when the quantum group is an ordinary compact group) are now only conjecturally equivalent. I will mention partial results relating these, as well as open questions.

3:00 pm in 243 Altgeld Hall,Thursday, November 12, 2015

Hyperplane Arrangement Complements - Topological Complexity and Zero-divisors-cup-length

Nathan Fieldsteel (UIUC Math)

Abstract: The topological complexity $TC(X)$ of a space $X$ is an integer which measures the difficulty of finding a continuous motion planning algorithm for that space. While $TC(X)$ can be very difficult to compute in general, a lower bound can be obtained by computing the zero-divisors-cup-length of the cohomology of $X$, and this bound is conjectured to be sharp in many cases. One such case is when $X$ is the complement of a complex arrangement of hyperplanes. Such spaces have combinatorially determined cohomology rings, called Orlik-Solomon algebras, and we will discuss some progress towards finding a combinatorial formula for the zero-divisors-cup-length of these algebras.

3:00 pm in 345 Altgeld Hall,Thursday, November 12, 2015

Spectral representation of semigroups of fractional type and hypocoercivity

Pierre Patie   [email] (Cornell University)

Abstract: In this talk, I will present an original methodology to develop the spectral representation of a class of Markov semigroups whose infinitesimal generators are non-self-adjoint and non-local. Its integral part can be expressed as a generalized fractional operator of Caputo type. Our approach is based on an in-depth study of an intertwining relationship that we establish between this class and a self-adjoint Markov semigroup for which the spectral reduction is well-know. For the class of invariant semigroups, we are able to provide precise information regarding the speed of convergence to stationarity. In particular, we observe in some cases the hypocoercivity phenomena which, in our context, can be interpreted in terms of the spectral norms. This talk is based on joint works with M. Savov and Y. Zhao.

3:00 pm in 347 Altgeld Hall,Thursday, November 12, 2015

Résumés for nonacademic job applications

Jennifer Kim   [email] (UIUC Graduate Career Development)

Abstract: An employer's first contact with you is often through your résumé. So how can you make your résumé stand out from the crowd? How can you present your academic experience as being relevant to a non-academic position? Mathematics graduate students and postdocs are welcome at this informal discussion.

4:00 pm in 245 Altgeld Hall,Thursday, November 12, 2015

From counting to quantum gravity

Steffen Rohde (University of Washington, Seattle)

Abstract: In how many ways can you draw a connected graph with n edges on the 2-dimensional sphere (up to homeomorphisms of the sphere, say)? How does such a map, chosen uniformly among all maps with n edges, "look like" when n gets large? Is there a "canonical" way to draw a given graph? And what would that look like for large n? We will discuss how Tuttes census (answering the first question) inspired bijections between maps and trees (leading to an answer of the second question), how Grothendiecks dessins d'enfants can be viewed as an answer to the third question, and what is believed to be the answer to--and what is known about--the fourth question. No familiarity with any of these objects will be assumed.