Seminar Calendar
for events the week of Saturday, April 19, 2014.

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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, April 14, 2014

Seminar on Applied Topology And Neighboring Areas
2:00 pm   in 147 Altgeld Hall,  Monday, April 14, 2014
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Submitted by hirani.
 Anil Hirani (UIUC Math)Computing Harmonic FormsAbstract: Harmonic forms are needed in numerical analysis to solve Poison’s equation — the most basic elliptic partial differential equation. After motivating this application I will describe several numerical algorithms for computing harmonic forms. Some of these rely on the computation of a homology or cohomology basis as a first step. This is joint work with Kaushik Kalyanaraman, Han Wang and Seth Watts.

Symplectic & Poisson Geometry Seminar
3:00 pm   in 145 Altgeld Hall,  Monday, April 14, 2014
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Submitted by jawatts.
 David Martinez Torres (PUC-Rio de Janeiro)Transverse Geometry of Codimension one Foliations Calibrated by Closed 2-FormsAbstract: A codimension one foliation is (topologically) taut if it admits a closed 1-cycle everywhere transverse to the foliation. The theory of taut foliations is extremely rich in dimension 3, however, it less satisfactory in higher dimensions. In this talk we will discuss a different generalization of 3-dimensional taut foliati- ons to higher dimensions inspired in symplectic geometry. These are codimension one foliations which admit a closed 2-form which makes every leaf a symplectic manifold. Our main result is that on an ambient closed manifold a foliation (of class at least C^1 in the transverse direction) admitting a 2-calibration has its transverse geometry encoded in a 3-dimensional foliated submanifold. This is joint work with Álvaro del Pino and Francisco Presas (ICMAT, Madrid)

Ergodic Theory
4:00 pm   in 241 Altgeld Hall,  Monday, April 14, 2014
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Submitted by jathreya.
 Kevin Pilgrim (Indiana)Are branched expanding maps $f: S^2 \to S^2$ smoothable?Abstract: Branched expanding maps $f: S^2 \to S^2$ generalize piecewise expanding multimodal maps of the interval and are the object of much recent study (Cannon-Floyd-Parry; Haissinsky-P.; Bonk-Meyer; Meyer; Nekrashevych). Typically, these are presented only indirectly, and one does not have any good "normal forms" for topological conjugacy classes, e.g. smooth, piecewise affine, etc. models. Are these subsumed in the theory of smooth dynamics? This ignorance contrasts greatly with what we know about expanding maps of circles, intervals, and (infra nil) manifolds. I will focus on several different ways of constructing examples: matings (with movies), subdivision rules (with pictures), contracting virtual endomorphisms of orbifold fundamental groups (with algebra formulas) and other rare examples (with exact formulas).

U of I WebStore Special Event
4:00 pm   in 165 Everitt Lab,  Monday, April 14, 2014
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Submitted by seminar.
 Wolfram|Alpha Pro and Mathematica 9Abstract: During this free seminar, explore using Mathematica and Wolfram|Alpha Pro for a wide variety of practical and theoretical applications across a variety of disciplines. Attendees will not only see new features in Wolfram|Alpha Pro and Mathematica 9, but will also receive examples of this functionality to begin using immediately. No Mathematica experience is required, and students are encouraged to attend. Register at http://webstore.illinois.edu/wolfram

Geometric Aspects of Supersymmetric Quantum Field Theories RAP
4:00 pm   in 143 Altgeld Hall,  Monday, April 14, 2014
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Submitted by katz.
 Sheldon Katz (Illinois Math)The (2,2) sigma model and its topological twistsAbstract: I begin by describing the sigma model with target a Kahler manifold X, a two-dimensional quantum field theory with (2,2) supersymmetry on a Riemann surface $\Sigma$. I then describe its topological twists, the A-model and the B-model. The A-model localizes on holomorphic maps $\phi:\Sigma\to X$ and its correlation functions are precisely the Gromov-Witten invariants if $\Sigma$ has genus 0. The B model localizes on constant maps, hence its correlation functions are given by integrals on X. Finally, I describe the setup of mirror symmetry, whereby enumerative invariants of curves on Calabi-Yau manifolds can be computed by classical integrals on a mirror Calabi-Yau manifold.

Operator Algebras Learning Seminar
5:00 pm   in 241 Altgeld,  Monday, April 14, 2014
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Submitted by longfie2.
 Ali Kavruk (UIUC Math)On Junge's ProblemAbstract: In quantum information, Peres–Horodecki criterion (positive partial transpose or PPT) is sufficient to determine separability of a quantum state when the underlying Hilbert space dimensions are low (2x2, 2x3, 3x2). Junge's problem states that, for any local dimension, bi-PPT quantum cones can be used to detect separability. In this talk we will focus on general theory of symmetrization in operator systems, and study their functorial properties. Then we will obtain some formulations of Junge's problem. We will also outline some connection with Tsirelson's problem in quantum information.

Tuesday, April 15, 2014

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by phierony.
 Thanases Pheidas (Purdue/University of Crete)Buchi's Problem and Uniform Undecidability for rings of functions of positive characteristicAbstract: We address the question: Is there an algorithm which can decide, given a polynomial equations (in many variables), with coefficients in F_p[z] (polynomials over z, with coefficients in the finite field with p elements, p a prime), whether the polynomial has solutions in F_p(z) for almost all primes p (or for infinitely many p, or for all primes p congruent to 1 mod 4)? We will present a negative answer to this question. A critical element of the proof is the solution to an analogue of Buchi's problem, a problem in Number Theory of independent interest.

Joint Differential Geometry and Group Theory Seminar
1:00 pm   in Altgeld Hall 243,  Tuesday, April 15, 2014
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Submitted by kapovich.
 Kasra Rafi (University of Toronto)Evolving structures and uniform growth rateAbstract: During his 60th birthday conference, Thurston asserted that the growth rate of mapping class group is independent of genus. In this talk, we attempt to understand why and to what extend this is true. It turns out, given the right choice of generating sets, the mapping class group, Out(F_n) and SL(n,Z) all have uniform growth rates. We use the ideas and the work of Sleator-Tarjan-Thurston.

Harmonic Analysis and Differential Equations (HADES)
1:00 pm   in 347 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by verahur.
 David Nicholls (UIC)Layered Media Scattering: Fokas Integral Equations and Boundary Perturbation MethodsAbstract: In this talk we describe a class of Integral Equations to compute Dirichlet-Neumann operators for the Helmholtz equation on periodic domains inspired by the recent work of Fokas and collaborators on novel solution formulas for boundary value problems. These Integral Equations have a number of advantages over standard alternatives including: (i.) ease of implementation (high-order spectral accuracy is realized without sophisticated quadrature rules), (ii.) seamless enforcement of the quasiperiodic boundary conditions (no periodization of the fundamental solution, e.g. via Ewald summation, is required), and (iii.) reduced regularity requirements on the interface proles (derivatives of the deformations do not appear explicitly in the formulation). We show how these can be efficiently discretized and utilized in the simulation of scattering of linear acoustic waves by families of periodic layered media which arise in geoscience applications.

Probability Seminar
2:00 pm   in Altgeld Hall 347,  Tuesday, April 15, 2014
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Submitted by kkirkpat.
 Qiang Zeng (UIUC Math)Poincar\'e inequalities in Noncommutative $L_p$ spacesAbstract: It is known in probability theory that good estimates of moments of random variables lead to concentration inequalities. The Poincar\'e inequalities provide upper bounds for the moments of random variables using their derivatives. In this talk, I will first give some motivating examples of $L_p$ Poincar\'e inequalities with satisfactory constants in classical probability and Fourier analysis. Then I will explain the consequences of these inequalities and a general theory in the context of noncommutative $L_p$ spaces. The talk is based on joint work with Marius Junge.

Descriptive Ergodic Theory Seminar
2:00 pm   in 241 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by anush.
 Canceled

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by nevins.
 Mihnea Popa (UIC Math)Holomorphic one-forms on varieties of general typeAbstract: I will explain recent work with C. Schnell, in which we prove that every holomorphic one-form on a variety of general type has non-empty zero locus (together with a suitable generalization to arbitrary Kodaira dimension). The proof makes use of generic vanishing theory for Hodge D-modules on abelian varieties.

Applied Mathematics
3:00 pm   in 347 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by bronski.
 Wendy K. Tam Cho (UIUC Political Science/Statistics)Replication and Optimization in Causal InferenceAbstract: A common thread throughout scientific endeavors is the desire to identify and understand causal relationships. Randomized experiments are the gold standard for isolating treatment effects and identifying causal relationships. When experiments are not practical or not possible, researchers sometimes turn to observational data. Matching methods comprise one strategy for making causal inferences with observational data. We present a new paradigm and method for making causal inferences in the absence of experimental data. Our method incorporates an optimization approach that illuminates important scientific notions of replication. While observational studies have obvious pitfalls, we demonstrate how our computational approach highlights previously unseen opportunities with these data.

Graph Theory and Combinatorics
3:00 pm   in 241 Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by lidicky.
 Sarka Petrickova (UIUC Math)Online Ramsey Theory for Planar GraphsAbstract: An online Ramsey game $(G,\mathcal{H})$ is a game between Builder and Painter, alternating in turns. During each turn, Builder draws an edge, and Painter colors it blue or red. Builder's goal is to force Painter to create a monochromatic copy of $G$, while Painter's goal is to prevent this. The only limitation for Builder is that after each of his moves, the resulting graph has to belong to the class of graphs $\mathcal{H}$. It was conjectured by Grytczuk, Haluszczak, and Kierstead (2004) that if $\mathcal{H}$ is the class of planar graphs, then Builder can force a monochromatic copy of a planar graph G if and only if G is outerplanar. Here we show that the only if'' part does not hold while the if'' part does.

4:00 pm   in Altgeld Hall,  Tuesday, April 15, 2014
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Submitted by villeta2.
 Matej Penciak (UIUC Math)Schemes as FunctorsAbstract: Replacing schemes with their functor of points offers a useful perspective to tackle moduli problems. In this talk I will explain this interpretation of schemes, characterize the functors that come from this construction, and try to motivate this viewpoint through various examples. Along the way I will discuss the Quot and Hilbert schemes--two schemes that represent common moduli problems.

Wednesday, April 16, 2014

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 16, 2014
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Submitted by laugesen.
 Richard Sowers (Department of Mathematics, University of Illinois at Urbana-Champaign)Hard to borrow (bankrupt) stocks

Thursday, April 17, 2014

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, April 17, 2014
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Submitted by ford.
 Andrew Snowden (Univ. Michigan Math)Integral structures on de Rham cohomologyAbstract: Give a smooth projective variety X over the function field K of a complex curve C, its algebraic de Rham cohomology forms a finite dimension K vector space. This vector space can be canonically realized as the generic fiber of a coherent sheaf on C, in two ways: one Hodge-theoretic and one geometric. I will explain an arithmetic version of this, where K is a number field. Here, p-adic Hodge theory takes the place of usual Hodge theory. This is joint work with Bhargav Bhatt.

Group Theory Seminar
1:00 pm   in Altgeld Hall 347,  Thursday, April 17, 2014
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Submitted by kapovich.
 Ilya Kapovich (UIUC Math)Patterson-Sullivan currents, generic stretch factors and the asymmetric Lipschitz metric for Outer spaceAbstract: We quantitatively relate the Patterson-Sullivant currents to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number. As an application we show that for any N\ge 2 there exists a positive constant C_N>0 such that for every \phi\in Out(F_N), where F_N=F(A)=F(a_1,..,a_N) is the free group of rank N, we have $C_N\le \lambda_A(\phi)/ \Lambda_A(\phi) \le 1$. Here $\Lambda_A(\phi)= \sup_{w\ne 1} ||\phi(w)||_A/||w||_A$ is the "extremal distortion" of $\phi$, and $\lambda_A(\phi)$ is the "generic stretching factor" of $\phi$, that is, $\lambda_A(\phi)$ is the asymptotic distortion $||\phi(w)||_A/||w||_A$ where $w$ is a "long random element" in $F(A)$, as $||w||_A\to\infty$. The talk is based on joint work with Martin Lustig.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, April 17, 2014
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Submitted by jvalidas.
 Xin Zhou (University of Michigan, Ann Arbor)Asymptotics of equivariant syzygiesAbstract: Recent results on syzygies concentrate on their asymptotics. In this talk, I will discuss results on the asymptotics of syzygies under group actions. In particular, we study two cases. When the underlying space is the projective space, we give the asymptotic growth of syzygy modules with respect to the general linear group. When the underlying space is a toric variety, we give a sharp asymptotic description of the distribution of torus weights.

Spring Department Faculty Meeting
4:00 pm   in 245 Altgeld Hall,  Thursday, April 17, 2014
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Submitted by seminar.
 Spring Department Faculty MeetingAbstract: The Spring Department Faculty Meeting will be held at 4 p.m. in 245 Altgeld Hall, followed by a reception in 243 Altgeld Hall.

Friday, April 18, 2014

 Ben Fulan (UIUC Math)Faces of PersistenceAbstract: Topological data analysis is a relatively new field that seeks to apply techniques from algebraic topology to problems that have traditionally been approached using statistical methods. One such problem is as follows: Given a set of points sampled randomly from a space $X$, can one recover the topological structure of $X$? A key technique that has been developed to address this question is persistent homology. We will give an introduction to this technique and compare different ways of presenting the resulting information, such as barcodes, persistence diagrams, and merge trees.
 Pantelis Eleftheriou (Universitaet Konstanz)Locally definable groups as covers of definable groupsAbstract: A locally definable group in an o-minimal structure is a group whose domain is a countable union of definable sets $U_i$ and whose multiplication is definable when restricted to each $U_i \times U_j$. An important example is the universal cover of a definable group. We examine the following converse. Conjecture. Let $U$ be a connected abelian locally definable group which is generated by a definable set. Then $U$ is a cover of a definable group. In this talk we will report progress on the status of this conjecture and mention a number of statements that are equivalent to it. (Joint work with Y. Peterzil)