Seminar Calendar
for events the week of Saturday, February 25, 2017.

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events for the
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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, February 20, 2017

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, February 20, 2017
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Submitted by laugesen.
 Richard Sowers (Department of Mathematics, University of Illinois)Stuck in TrafficAbstract: Used Uber or Lyft lately? Been in a traffic jam lately? There is an increasing amount of interest and data in making 'cities' and 'mobility' smart. We take a look at some data and data reduction problems which we have been looking at for the past several months. We outline some current and new challenges. This is work with Professor Dan Work of Civil and Environmental Engineering, the PI4 program, and the IGL program.

Operator Algebra Learning Seminar
5:00 pm   in 241 Altgeld Hall,  Monday, February 20, 2017
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Submitted by clinden2.
 Chris Linden (UIUC Math)Quasidiagonality of Nuclear C*-AlgebrasAbstract: Tikuisis, White, and Winter have shown that faithful traces on separable, nuclear C*-algebras which satisfy the UCT are quasidiagonal. As a corollary, the reduced group C*-algebra of an amenable group is quasidiagonal. I will discuss Schafhauser's recent proof of this theorem using the extension theory of C*-algebras.

Tuesday, February 21, 2017

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 243 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by clein.
 John P. D'Angelo (Illinois Math)Groups Associated with Rational Proper MapsAbstract: Given a rational proper map $f$ between balls of typically different dimensions, we define a subgroup $\Gamma_f$ of the source automorphism group. We prove that this group is noncompact if and only if $f$ is linear. We show how these groups behave under certain constructions such as juxtaposition and partial tensor products. We then sketch a proof of the following result. If $G$ is an arbitrary finite subgroup of the source automorphism group, then there is a rational map $f$ for which $\Gamma_f = G$. We provide many examples and, if time permits, discuss the degree estimate conjecture. This work is joint with Ming Xiao.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by anush.
 Erik Walsberg (UIUC Math)"Strong theories of ordered abelian groups" by A. Dolich and J. Goodrick (2nd talk)

Several Complex Variables and CR Geometry Seminar
2:00 pm   in 243 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by mingxiao.
 Jeffery McNeal (The Ohio State University)L^2 extension of d-bar closed forms from hypersurfacesAbstract: Extending holomorphic functions off of hypersurfaces, with L^2 control, was initiated by pioneering work of Ohsawa and Takegoshi in the late 80s. The original extension results have been greatly generalized, as there are numerous application of such results to problems in analytic geometry. Less is known about extending higher order forms. I will discuss some new results about extension of d-bar closed forms with L^2 estimates. The talk will start with the simplest extension set-up -- a domain in C^n, a hyperplane and functions -- then add apparatus slowly-- moving to manifolds, bundle-valued forms, and curvature conditions. The results discussed were obtained in collaboration with Dror Varolin.

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by molla.
 Douglas B. West (Illinois Math and Zhejiang Normal University)Reconstruction from the deck of $k$-vertex induced subgraphsAbstract: The $k$-deck of a graph is its multiset of subgraphs induced by $k$ vertices; we ask whether the $k$-deck determines the graph. We show that a complete $r$-partite graph is determined by its $(r+1)$-deck. Letting $n=|V(G)|$, we generalize a result of Bollobás by showing that for $l=(1-o(1))n/2$, almost every graph $G$ is determined by various sets of ${l+2\choose 2}$ subgraphs with $n-l$ vertices. However, when $l=n/2$, the entire $(n-l)$-deck does not always determine whether $G$ is connected (it fails for $n$-vertex paths). We strengthen a result of Manvel by proving for each $l$ that when $n$ is sufficiently large (at least $l^{l^2}$), the $(n-l)$-deck determines whether $G$ is connected ($n\ge25$ suffices when $l=3$, and $n\le 2l$ cannot suffice). Finally, for every graph $G$ with maximum degree $2$, we determine the least $k$ such that $G$ is reconstructible from its $k$-deck, which involves extending a result of Stanley. This is joint work with Hannah Spinoza.

4:00 pm   in 245 Altgeld Hall,  Tuesday, February 21, 2017
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Submitted by laugesen.
 Reinhard Laubenbacher and Anna Konstorum   [email] (Center for Quantitative Medicine, University of Connecticut)From Computational Algebra to Quantitative MedicineAbstract: In this informal discussion conducted by Skype, the panelists from the Center for Quantitative Medicine at the University of Connecticut will describe their career paths from mathematics into medicine, and then take questions from the audience. Background: Prof. Laubenbacher spent most of his career working in computational algebra and discrete mathematics. Dr. Konstorum's thesis work was in differential equations. All are welcome to participate in this career event!

Wednesday, February 22, 2017

Doob Colloquium
3:00 pm   in 243 Altgeld Hall,  Wednesday, February 22, 2017
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Submitted by lescobar.
 Mark Bell (UIUC)Topology in dimensions 1, 2 and 3Abstract: We will look at some of the surprising connections between low-dimensional manifolds. In particular, we will focus on the classification problem, which aims to build a periodic table of all manifolds up to homeomorphism. To tackle some of the difficulties of doing this in dimension 3, we will resort to looking at lower dimensional submanifolds and how they sit inside.

Thursday, February 23, 2017

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by sahlgren.
 Amita Malik (Illinois Math)Partitions into $k$th powers of a fixed residue classAbstract: G. H. Hardy and S. Ramanujan established an asymptotic formula for the number of unrestricted partitions of a positive integer, and claimed a similar asymptotic formula for the number of partitions into perfect $k$th powers, which was later proved by E. M. Wright. In this talk, we discuss partitions into parts from a specific set $A_k(a_0,b_0) :=\left\{ m^k : m \in \mathbb{N}, m\equiv a_0 \pmod{b_0} \right\}$, for fixed positive integers $k$, $a_0,$ and $b_0$. We give an asymptotic formula for the number of such partitions, thus generalizing the results of Wright and others. We also discuss the parity problem for such partitions. This is joint work with Bruce Berndt and Alexandru Zaharescu.

Analysis Seminar
2:00 pm   in Altgeld Hall,  Thursday, February 23, 2017
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Submitted by tumanov.
 Bruce Reznick (UIUC)Inequalities for products of power sums and the classical moment problem.Abstract: This is a partial repeat of a seminar I gave here in the early 1980s. For $x = (x_1,\dots x_n) \in \mathbb R^n$ and $r \in \mathbb N$, define the $r$-th power sum $M_r(x) = \sum_{i=1}^n x_i^r$. Upper bounds for many products of power sums come from the Hölder and Jensen inequalities. I will discuss some other cases: for example $M_1M_3/(nM_4)>-\frac 18$, where the lower bound is best possible, and the maximum and minimum values of $M_1M_3/M_2^2$ are $\pm \frac{3\sqrt 3}{16}n^{1/2} + \frac 58 + \mathcal O(n^{-1/2})$. In the first case, the classical Hamburger moment problem gives a particularly illuminating explanation. Most of this can be found in my paper: Some inequalities for products of power sums, Pacific J. Math., 104 (1983), 443-463 (MR 84g.26015), available at https://projecteuclid.org/euclid.pjm/1102723674

2:00 pm   in 241 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by amalik10.
 Dane Skabelund   [email] (UIUC)Some maximal curves obtained via a ray class field constructionAbstract: This talk will be about curves over finite fields which are "maximal" in the sense that they meet the Hasse-Weil bound. I will describe some problems relating to such curves, and give a description of some new "maximal" curves which may be obtained as covers of the Suzuki and Ree curves.

Algebra, Geometry and Combinatorics Seminar
3:00 pm   in 347 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by lescobar.
 Bennet Goeckner (The University of Kansas)A non-partitionable Cohen-Macaulay complexAbstract: Stanley conjectured in 1979 that all Cohen-Macaulay complexes were partitionable. We will construct an explicit counterexample to this conjecture, which also disproves a related conjecture about the Stanley depth of monomial ideals. This talk is based on joint work with Art Duval, Caroline Klivans, and Jeremy Martin. No prerequisite knowledge of simplicial complexes or commutative algebra will be assumed.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 23, 2017
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Submitted by kapovich.
 Pekka Pankka (University of Helsinki)From Picard to Rickman: Mappings in spatial quasiconformal geometryAbstract: One of the classical theorems in complex analysis is the Picard’s theorem stating that a non-constant entire holomorphic map from the complex plane to the Riemann sphere omits at most two points. From the conformal point of view, two dimensional geometry is special in this sense. Namely, by classical Liouville’s theorem from the same era, every conformal map from a domain of the n-sphere to the n-sphere is a restriction of a Möbius transformation for n>2. In particular, Picard’s theorem holds trivially in higher dimensions. An alternative for the overly rigid spatial conformal geometry is a so-called quasiconformal geometry; heuristically, instead of preserving the angles we allow them to distort by a bounded amount. In this talk, I will discuss the role of Picard’s theorem in quasiconformal geometry, which takes us from complex analysis to geometric topology.

Friday, February 24, 2017

3:00 pm   in 243 Altgeld Hall,  Friday, February 24, 2017
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Submitted by jjwen2.
 Sungwoo Nam (UIUC Math)Quantum cohomology of Grassmannians and Gromov-Witten invariantsAbstract: As a deformation of classical cohomology ring, (small) quantum cohomology ring of Grassmannians has a nice description in terms of quantum Schubert classes and it has (3 point, genus 0) Gromov-Witten invariants as its structure constants. In this talk, we will describe how 'quantum corrections' can be made to obtain quantum Schubert calculus from classical Schubert calculus. After studying its structure, we will see that the Gromov-Witten invariants, which define ring structure of quantum cohomology of Grassmannians, are equal to the classical intersection number of two-step flag varieties. If time permits, we will discuss classical and quantum Littlewood-Richardson rule using triangular puzzles.

4:00 pm   in 241 Altgeld Hall,  Friday, February 24, 2017
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Submitted by dcarmod2.
 Bill Karr (UIUC Math)Geometry of convex hypersurfacesAbstract: A convex hypersurface in Euclidean space or Minkowski space is the boundary of an open convex set. Smooth convex hypersurfaces have non-negative sectional curvature and indicate properties of more general Riemannian manifolds with non-negative curvature. I will discuss some properties of convex hypersurfaces. Finally, I will describe a problem that arises from Lorentzian geometry involving convex hypersurfaces and geodesic connectedness and discuss a possible solution to this problem.

Model Theory and Descriptive Set Theory Seminar
4:00 pm   in 345 Altgeld Hall,  Friday, February 24, 2017
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Submitted by anush.
 Aristotelis Panagiotopoulos (UIUC Math)On "Structurable equivalence relations" by R. Chen and A. Kechris: Structurability by structures with TDC (4th talk)Abstract: In this talk, we prove a theorem of A. Marks included in the current paper. It says that every aperiodic countable Borel equivalence relation can be $\mathcal{A}$-structured for any countable structure $\mathcal{A}$ with trivial definable closure (TDC). Examples include the rationals, the random graph, and the rational Urysohn sphere.

Department Social Hour
4:30 pm   in 239 Altgeld Hall,  Friday, February 24, 2017
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Submitted by seminar.
 Department Social HourAbstract: The department will host a social hour from 4:30-5:30 pm in 239 Altgeld Hall. This is an opportunity for all members of the department to meet and exchange ideas.