Seminar Calendar
for events the week of Monday, October 24, 2016.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, October 24, 2016

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, October 24, 2016
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Submitted by laugesen.
 Xiaochun Li (Department of Mathematics, University of Illinois)Some Radon transforms and their discrete analogueAbstract: We report some progress on certain Radon transforms and some discrete analogue. For instance, bilinear Hilbert transform along curves, discrete Strichartz estimate and its relation with weighted restriction, etc.

Symplectic & Poisson Geometry Seminar
4:00 pm   in 241 Altgeld Hall,  Monday, October 24, 2016
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Submitted by jpascale.
 Mark McLean (Stony Brook University)The Cohomological McKay Correspondence and Symplectic CohomologyAbstract: Suppose that we have a finite quotient singularity C^n/G admitting a crepant resolution Y (i.e. a resolution with c_1 = 0). The cohomological McKay correspondence says that the cohomology of Y has a basis given by irreducible representations of G (or conjugacy classes of G). Such a result was proven by Batyrev when the coefficient field F of the cohomology group is Q. We give an alternative proof of the cohomological McKay correspondence in some cases by computing symplectic cohomology+ of Y in two different ways. This proof also extends the result to all fields F whose characteristic does not divide |G| and it gives us the corresponding basis of conjugacy classes in H^*(Y). We conjecture that there is an extension to certain non-crepant resolutions. This is joint work with Alex Ritter.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, October 24, 2016
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Submitted by ligao3.
 Li Gao (UIUC Math)Renyi Divergence and Noncommutative $L_p$ spacesAbstract: We continue from last time.

Tuesday, October 25, 2016

Topology Seminar
11:00 am   in 345 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by rezk.
 Nitu Kitchloo (Johns Hopkins)Quantization of the Modular Functor and Equivariant Elliptic CohomologyAbstract: For a simple, simply connected compact Lie group G, let M be a compact G-space. I will describe a procedure that can be interpreted as the quantization of the category of parametrized positive energy representations of the loop group of G at a given level. This procedure is described in terms of dominant K-theory of the loop group parametrized over M. More concretely, I will construct a holomorphic sheaf over a universal elliptic curve with values in dominant K-theory of the loop space LM, and show that each stalk of this sheaf is a cohomological functor of M.I will also give compelling evidence that this theory is equivalent to equivariant elliptic cohomology of M as constructed by Grojnowski. In this talk, I will try to start from basics and give ample motivation.

Geometry, Groups, and Dynamics/GEAR
12:00 pm   in 243 Altgeld Hall,  Tuesday, October 25, 2016
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 Marina Logares (Oxford University)Character Varieties and the Hodge Monodromy RepresentationAbstract: Character varieties have been studied thoroughly in relation with moduli spaces of Higgs bundles. Their topological invariants where studied via the non abelian Hodge correspondence, and recently attention has been focused on the so called e-polynomial, which provides algebraic information on them. I'm going to report on ongoing work on formalising the method to compute e-polynomials given in joint work with P. Newstead and V. Muñoz. This formalisation is intended for producing a 1+1 TQFT, this is a project with A. González and V. Muñoz

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by ssolecki.
 Justin Moore (Cornell University)The subgroup structure of Richard Thompson's group FAbstract: Consider the finitely generated subgroups of F, ordered by embeddability. How complex is it? Is it a well quasi-order? We show that it contains a strictly well ordered chain of length $\epsilon_0 +1$. This is joint work with Collin Bleak and Matt Brin.

Harmonic Analysis and Differential Equations (HADES)
1:00 pm   in 347 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by berdogan.
 Ebru Toprak (UIUC Math)Dispersive estimates for Dirac operators in dimension threeAbstract: In this talk, we discuss $L^1\to L^\infty$ dispersive estimates for the three dimensional Dirac equation with a potential. We classify the structure of obstructions at the thresholds of the essential spectrum as being composed of a two dimensional space of resonances and finitely many eigenfunctions. We show that, as in the case of the Schr\"odinger evolution, the presence of a threshold obstruction generically leads to a loss of the natural $t^{-\frac32}$ decay rate. In this case we show that the solution operator is composed of a finite rank operator that decays at the rate $t^{-\frac12}$ plus a term that decays at the rate $t^{-\frac32}$.

2:00 pm   in 241 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by jli135.
 Paulina Koutsaki (UIUC )Some results related to the distribution of zeros of a family of Dirichlet series.Abstract: Let $G(s)=\sum\limits_{n=1}^{\infty} a_n \,n^{-s}$ be a Dirichlet series with coefficients bounded by $n^{\epsilon}$ for every $\epsilon>0$, and define $\beta_{k,G}$ to be the supremum of the real parts of zeros of combinations of $G$ and its $k$ first derivatives. In this talk, we give an asymptotic formula for the number $\beta_{k,G}$ and investigate in more detail the case of Dirichlet L-functions. We will also discuss an inverse-type problem for the Riemann-zeta function. In particular, we compute the degree of the largest derivative needed for such a combination to vanish at a given real number. For example, a combination that vanishes at $\beta=1,000,000$ will involve a derivative of order at least 2,178,301. This is joint work with A. Tamazyan and A. Zaharescu.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by rtramel.
 Jonathan Wang (University of Chicago)A strange bilinear form on the space of automorphic formsAbstract: Let F be a function field and G a reductive group over F. We define a "strange" bilinear form B on the space of K-finite smooth compactly supported functions on G(A)/G(F). For G = SL(2), the definition of B generalizes to the case where F is a number field (and this is expected to be true for any G). The definition of B relies on the constant term operator and the standard intertwining operator. This form is natural from the viewpoint of the geometric Langlands program via the functions-sheaves dictionary. To see this, we show the relation between B and S. Schieder's geometric Bernstein asymptotics.

Graph Theory and Combinatorics Semianr
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by molla.
 Sarah Loeb (Illinois Math)Fractional Separation DimensionAbstract: Given a linear ordering $\sigma$ of $V(G)$, say that a pair of nonincident edges is separated by $\sigma$ if both vertices of one edge precede both vertices of the other. The separation dimension is the minimum size of a set of vertex orders needed to separated every pair of non-incident edges. The $t$-separation dimension $\pi_t(G)$ of a graph $G$ is the minimum size of a multiset of vertex orders needed to separate every pair of non-incident edges of $G$ $t$ times. The fractional separation dimension $\pi_f(G)$ of a graph $G$ is $\liminf_t \pi_t(G)/t$. We show that $\pi_f(G)\le 3$ for every graph $G$, with equality if and only if $K_4\subseteq G$. On the other hand, there is no sharper upper bound; we show $\pi_f(K_{m,m})=\frac{3m}{m+1}.$ This is joint work with Douglas West.

Illinois Geometry Lab
5:00 pm   in 245 Altgeld Hall,  Tuesday, October 25, 2016
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Submitted by seminar.
 IGL Mid-semester MeetingAbstract: Mid-semester progress meeting for IGL project teams.

Wednesday, October 26, 2016

Descriptive Set Theory Learning Seminar
2:00 pm   in 443 Altgeld Hall,  Wednesday, October 26, 2016
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Submitted by anush.
 Anton Bernshteyn (UIUC Math)Measurable versions of the Lovász Local Lemma and measurable graph colorings, Part VAbstract: We will continue working through the paper "Measurable versions of the Lovász Local Lemma and measurable graph colorings" by Anton Bernshteyn.

Thursday, October 27, 2016

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, October 27, 2016
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Submitted by sahlgren.
 Ae Ja Yee (Penn State)Singular overpartitionsAbstract: Singular overpartitions, which were defined by George Andrews, are overpartitions whose Frobenius symbols have at most one overlined entry in each row. In his paper, Andrews obtained interesting results on singular overpartitions; in particular, one result relates a certain type of singular overpartitions with a subclass of overpartitions. In this talk, I will introduce partitions with dotted parity blocks and give a combinatorial proof of Andrews' result. I will also discuss some refinements on Andrews' result.

Department of Mathematics Retiree's Luncheon
11:30 am   in Urbana Country Club,  Thursday, October 27, 2016
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Submitted by seminar.
 Department of Mathematics Retiree's Luncheon

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, October 27, 2016
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Submitted by katz.
 Daliang Li (Johns Hopkins Physics)Conformal Bootstrap in the Lightcone LimitAbstract: The modern revival of conformal bootstrap has provided a new window into the strongly coupled dynamics of quantum field theories and the dual quantum gravitational theories. In this talk, we will explore universal structures of conformal field theories emerging from the conformal bootstrap in the lightcone limit. We start by reviewing the analysis of a 4-point function of real scalars, showing the existence of large spin, double-twist operators in unitary CFTs in d>2. These operators correspond to two-particle bound states in AdS and their anomalous dimensions correspond to the binding energies between the two particles. I will demonstrate the features of the binding energies arising from gauge and gravitational interactions. Then, using the 4-point function involving conserved currents and the stress energy tensor, I will establish a relation between the energy flux positivity in CFT and the attractiveness of gravity at large distances in AdS. Finally, I will use the bootstrap method to prove the conformal collider bounds for all unitarity CFTs in d>2.

Mathematical Biology Seminar
1:00 pm   in 347 Altgeld Hall,  Thursday, October 27, 2016
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Submitted by redavid2.
 Bo Lin   [email] (UC Berkeley)Convexity in Tree SpacesAbstract: We study the geometry of metrics and convexity structures on the space of phylogenetic trees, which is here realized as the tropical linear space of all ultrametrics. The ${\rm CAT}(0)$-metric of Billera-Holmes-Vogtman arises from the theory of orthant spaces. While its geodesics can be computed by the Owen-Provan algorithm, geodesic triangles are complicated. We show that the dimension of such a triangle can be arbitrarily high. Tropical convexity and the tropical metric behave better. They exhibit properties desirable for geometric statistics, such as geodesics of small depth. This is a joint work with Bernd Sturmfels, Xiaoxian Tang and Ruriko Yoshida.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 27, 2016
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Submitted by mastroe2.
 Winfried Bruns (University of Osnabrück)Castelnuovo-Mumford regularity of power productsAbstract: We show that the Castelnuovo-Mumford regularity and related invariants of products of powers of ideals in a standard graded polynomial ring are affine-linear in the exponents if these are large enough, provided that each ideal is generated by elements of constant degree. A counterexample shows that linearity is false without the condition, but the regularity is always given by the maximum of finitely many affine-linear polynomials. This is joint work with Aldo Conca (Genoa).

3:00 pm   in 441 Altgeld Hall,  Thursday, October 27, 2016
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Submitted by jjwen2.
 Lutian Zhao (UIUC Math)The Gopakumar-Vafa InvariantsAbstract: In 1998, Gopakumar and Vafa argued from M-theory that BPS counts (now known as Gopakumar-Vafa invariants) have the same "generating function" as the Gromov-Witten invariants. In particular, these invariants are integral, and they agree with naive curve counting in many cases. Also, it explains the contribution of multicovering and bubbling phenomena. The basic idea of this counting is to use Lefschetz decomposition on the moduli space of D-Branes to "virtually count" the number of abelian varieties. In this talk, I will discuss why it is a promising counting invariant and give some easy cases of this counting. The serious difficulty of this counting is the definition of moduli of D-Branes, which only have a satisfactory description at g=0. If time permits, I will describe some attempts by Hosono-Saito-Takahashi, Kiem-Li and Maulik-Toda on this theory.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 27, 2016
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Submitted by kapovich.
 Ae Ja Yee (Pennsylvania State University)The smallest parts function and the third order mock theta function $\omega(q)$Abstract: The smallest parts function spt$(n)$, counting the total number of appearances of the smallest parts in all partitions of $n$, has received great attention since it was first introduced by George Andrews in 2007. In this talk, I will give an introduction to and brief history of this subject. I will also discuss some recent discoveries in connection to the mock theta function $\omega(q)$. This is joint work with G. E. Andrews, A. Dixit, D. Passary, D. Schultz, J. Sellers and L. Wang.

Friday, October 28, 2016

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, October 28, 2016
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Submitted by anush.
 Erik Walsberg (UIUC Math)First order expansions of the realsAbstract: We discuss what we understand of the classification of first order expansions of $(\mathbb{R},<,+)$ according to the topology and geometry of their definable sets.

Saturday, October 29, 2016

Mathematics Homecoming Party
2:00 pm   in tent out front of Altgeld Hall,  Saturday, October 29, 2016
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Submitted by seminar.
 Mathematics Homecoming Party Abstract: Department of Mathematics Homecoming Party will be held Saturday, October 29, 2016, from 2:00-4:00 pm. Look for our tent in front of Altgeld Hall. A complimentary buffet will be available to all our alumni. Please plan to attend and welcome our alumni back to campus!