Seminar Calendar
for events the week of Friday, October 9, 2015.

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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 5, 2015

Math 499: Introduction to Graduate Mathematics
4:00 pm   in 245 Altgeld Hall,  Monday, October 5, 2015
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Submitted by laugesen.
 Maarten Bergvelt (Department of Mathematics, University of Illinois)Integrable Systems and Representation TheoryAbstract: "Special" functions are functions that at last some mathematicians care about. Experience has shown that many (all?) special functions come from representation theory and are solutions of integrable systems. A gentle introduction and examples are given.

4:00 pm   in 145 Altgeld Hall,  Monday, October 5, 2015
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Submitted by jjwen2.
 Yun Shi (UIUC Math)A geometric construction of moduli spaces of semistable sheavesAbstract: Classification of vector bundles is an important problem in algebraic geometry. It naturally leads to the study of moduli spaces of bundles. To obtain a nice scheme structure for the moduli spaces, one restricts the objects of interest to semistable bundles. Through the compactification of the moduli spaces, one naturally encounters non-locally free sheaves. In this talk, we will introduce a geometric construction of moduli spaces of semistable sheaves. By showing stability condition for coherent sheaves and stable points in the GIT sense amount to the same constraint, we construct the moduli space of semistable sheaves as a GIT quotient of an open subscheme of the Quot-scheme.

4:00 pm   in 141 Altgeld Hall,  Monday, October 5, 2015
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Submitted by anush.
 Anton Bernshteyn (UIUC Math)Forcing and Baire category: continuedAbstract: Forcing is a powerful tool invented by Paul Cohen for proving consistency and independence results. As we will see, forcing can be construed as a clever way to use Baire category. In this talk we will outline the method and its application to the independence of the Continuum Hypothesis from ZFC.

Literature Seminar in Operator Algebras
5:00 pm   in 241 Altgeld Hall,  Monday, October 5, 2015
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Submitted by fboca.
 Gao Li (UIUC Math)Lp estimates on quantum channelsAbstract: Quantum channels are completely positive trace preserving (CPTP) maps. I will talk about some Lp norm estimates on "nice" classes of CPTP maps. This is a joint work with Marius Junge and Nicholas LaRacuente. The main tools we use are Haagerup tensor product, GNS construction and complex interpolation. If time permits, I will present some connections to quantum information theory.

Tuesday, October 6, 2015

Geometry, Groups and Dynamics/GEAR Seminar
12:00 pm   in 345 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by clein.
 Valentina Disarlo (Indiana Math)Combinatorial rigidity of the arc complexAbstract: We study the arc complex of a surface with marked points in the interior and on the boundary. We prove that the isomorphism type of the arc complex determines the topology of the underlying surface, and that in all but a few cases every automorphism is induced by a homeomorphism of the surface. This generalizes a result of Irmak - McCarthy. As an application we deduce some rigidity results for the Fomin-Shapiro-Thurston cluster algebra associated to a surface. Our proofs do not employ any known simplicial rigidity result.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Tuesday, October 6, 2015
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Submitted by katz.
 Damian A. Galanti (Perimeter Institute for Theoretical Physics)Universal scaling properties after a Quantum QuenchAbstract: We will present the problem of a quantum quench in QFT, i.e., following the real-time evolution of an operator whose coupling is time dependant. Inspired by results in holography, we propose certain universal scaling properties that appear for fast and smooth quenches. We provide evidence for it in free scalar and fermionic field theories and provide a general argument of why the scaling should hold in arbitrary interacting CFTs. We also speculate on universal behaviour emerging for slow quenches through a critical point. Based on 1401.0560, 1411.7710, 1505.05224 and work in progress.

Several Complex Variables and CR Geometry
1:00 pm   in 241 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by jpda.
 Aaron Peterson (Northwestern)CR Control Geometry on Unbounded Domains in ${\mathbb C}^2$Abstract: Let $\Omega\subset \mathbb{C}^2$ be a weakly pseudoconvex finite-type domain with smooth boundary. We will discuss the Carnot-Carath\'eodory control geometry induced on ${\rm b}\Omega$ by the real and imaginary parts of the CR vector field, which has been used to describe the behavior of various objects associated to the $\bar{\partial}$- and $\bar{\partial}_b$-problems. After reviewing the local theory, we will develop a framework for studying this geometry on certain unbounded model domains. We will explore examples of unbounded domains where the global structure of the control geometry is vastly different than the local structure, and discuss a subclass of such examples where the control geometry still describes objects associated to the $\bar{\partial}$- and $\bar{\partial}_b$-problems.

Logic Seminar
1:00 pm   in 345 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by anush.
 Ward Henson   [email] (UIUC Math)Axiomatizing classes of Banach spacesAbstract: The context is first order logic for metric structures, applied to (unit balls of) Banach spaces and their expansions. Using this logic, many classes of Banach lattices are known to be axiomatizable. However, relatively few of the associated classes of Banach spaces have been similarly understood. With Yves Raynaud, we have developed some new techniques for transferring axiomatizability of suitable classes of Banach lattices to their Banach space reducts. The techniques involve facts about disjointness preserving linear isometries (between Banach lattices) from functional analysis, and facts about definability, especially definability of sets, from continuous model theory.

Probability Seminar
2:00 pm   in 347 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by psdey.
 Roger Lee   [email] (University of Chicago)Variance Swaps on Time-Changed Markov ProcessesAbstract: Relationships between, on one hand, expectations of random variables dependent on the path of a process X, and on the other hand, expectations of path-independent random variables that depend only on X_T for a fixed time T, have applications in finance, as they relate the prices of complex derivative contracts to the prices of basic derivative contracts. Consider the case of a "variance swap", in which the path-dependent random variable is quadratic variation of the log of a positive martingale -- given here by a Markov process, time-changed by a general continuous stochastic clock, which is allowed to depend on the driving Markov process, which is allowed to have state-dependent jump distributions. We show that the path-independent random variable can be chosen as G(X_T) if G satisfies an ordinary integro-differential equation, which depends only on the dynamics of the Markov process, not on the clock. In some examples, G can be computed explicitly.

Algebraic Geometry Seminar
3:00 pm   in 243 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by jccl.
 Justin Hilburn (University of Oregon)Boundary Conditions in QFT and Modules in Category OAbstract: By now it is well known that many features of the representation theory of semisimple Lie algebras can in fact be generalized to to any noncommutative algebra that arises as the quantization of functions on a symplectic cone. In particular for any such algebra there is an analogue of the BGG category O. These varieties seem to appear in "symplectic dual" pairs such that the associated pair of categories O are Koszul dual. In the 90s physicists described all known pairs of dual symplectic cones as the Higgs and Coulomb branches of the moduli space of vacua in 3d N=4 SUSY field theories, but they did not study the associated categories O. In this talk I will describe some work in progress with Bullimore, Dimofte, and Gaiotto to explain symplectic duality by studying boundary conditions in the associated field theory. In particular, I will describe an interesting construction of projective modules in category O for an abelian theory (aka Hypertoric Category O).

Graph Theory and Combinatorics Seminar
3:00 pm   in 241 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by molla.
 Adam Zsolt Wagner   [email] (UIUC Math)Tutorial on the Container MethodAbstract: Many important theorems and conjectures in combinatorics can be rephrased as problems about counting independent sets in some specific graphs and hypergraphs. The Container Method, whose basic idea can be traced back to Kleitman-Winston, and has recently been further developed by Balogh-Morris-Samotij and Saxton-Thomason, essentially states that hypergraphs satisfying some natural conditions have very few independent sets. In this survey-style talk I will show some recent applications of the method, and try to give an easy recipe containing all the key ideas one needs to know to prove similar results.

Mathematics in Science and Society (MSS)
4:00 pm   in 245 Altgeld Hall,  Tuesday, October 6, 2015
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Submitted by seminar.
 Roger Lee (University of Chicago)The wrong number to plug into the wrong formula to get the right price of a stock optionAbstract: Traders of stock options often quote prices not in dollars and cents, but rather in "implied volatility" -- sometimes described as "the wrong number to plug into the wrong formula to get the right price". We define what this means and explore why this makes sense, in the context of stochastic models of financial asset prices.

4:00 pm   in 149 Henry building,  Tuesday, October 6, 2015
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Submitted by emduart2.
 Amita Malik (UIUC)Number Theory in its various avatarsAbstract: In this talk, we will discuss certain number theoretic ubiquitous tools and see some examples on how they can be used to attack various problems lying at the interface of number theory and other mathematical areas. We will see how some deceptively simple looking problems are related to certain very well known problems. This talk can be thought of as an $\epsilon$-window into the mind of a number theorist. No prior knowledge will be assumed.

Wednesday, October 7, 2015

Integrability and Representation Theory (IRT)
3:00 pm   in 345 Altgeld Hall,  Wednesday, October 7, 2015
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Submitted by rinat.
 P. Di Francesco (UIUC)From Cluster Algebra to DAHA IIAbstract: We show a connection between the Berenstein-Zelevinsky quantum Cluster Algebra behind the Q-system and Cherednik’s Double Affine Hecke Algebras, the algebraic framework for symmetric and non-symmetric Macdonald polynomials and the theory of torus knot invariants.

PI4 Presentations
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 7, 2015
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Submitted by laugesen.
 Various Math graduate students   [email] (UIUC Mathematics)Abstract: All are welcome to come and enjoy these short presentations from students in the PI4 program from Summer 2015. The talks cover industrial and scientific internships and the on-campus working groups. Refreshments provided. Drop in and out of the room between talks as needed. Time: 4-6pm.

Thursday, October 8, 2015

Department of Mathematics Corporate Forum
9:00 am   in Illini Rooms A & B, Illini Union,  Thursday, October 8, 2015
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Submitted by seminar.
 Corporate ForumAbstract: The Corporate Forum will be held from 9 a.m. to 4 p.m. The Corporate Forum will be held from 9 a.m. to 4 p.m. Students majoring in Mathematics, Math/CS, Actuarial Science, and Statistics are invited to attend the 3rd Annual Mathematics Corporate Forum. Students will be able to engage with employers during this career fair/information session combination. The career fair will be held 9 am–4 pm (closed for lunch from noon–1 pm). Company presentations will be held throughout the day. See schedule at http://www.math.illinois.edu/UndergraduateProgram/math-career-fair.html

Number Theory Seminar
11:00 am   in 241 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by sahlgren.
 Nicolas Robles (UIUC Math)Mollifications of the Riemann zeta-function and families of $L$-functionsAbstract: We explain how by twisting the a mean value integral of the Riemann zeta-function by a suitable Dirichlet polynomial we can generate interesting results about the proportion of non-trivial zeros on the critical line. By using sieve results of Conrey, Iwaniec and Soundararajan, this mollification process can yield better results (over 50%) for certain averages of $L$ functions up to degree 3. This is joint work with Dirk Zeindler, Arindam Roy and Alexandru Zaharescu.

Math-Physics Seminar
12:30 pm   in 464 Loomis Laboratory,  Thursday, October 8, 2015
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Submitted by katz.
 Dean Carmi (Tel-Aviv Physics)Shape dependence and RG flow of entanglement entropyAbstract: I will describe the results of two recent papers on entanglement entropy (EE). In the first paper we study the shape dependence of EE. We start with symmetric entangling surfaces and slightly deform them, and we compute the resulting corrections to the EE. In the second paper we study EE on a sphere. We obtain a few analytical results, and discuss the connection to RG flows and c-theorems.

Geometry, Groups and Dynamics/GEAR Seminar
1:00 pm   in 243 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by clein.
 Robert Tang (Oklahoma Math)Shadows of Teichmueller discs in the curve graphAbstract: A Teichmueller disc parameterises the family of metrics obtained by performing SL(2,R)-deformations on a given flat surface. We consider several natural sets of curves associated with a Teichmueller disc from the point of view of the curve graph. We show that these sets agree up to uniform Hausdorff distance, and are all quasiconvex. Furthermore, we extend the notion of balance time along Teichmueller geodesics to Teichmueller discs, and show that it satisfies analogous projection properties to the curve graph. This talk will focus on the tools used to prove the above results. This is a joint work with Richard Webb.

Analysis Seminar
2:00 pm   in 243 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by tumanov.
 Florent Baudier (Texas A&M)Embeddability of graphs into Banach spacesAbstract: We will discuss several results about the bi-Lipschitz embeddability of certain families of graphs (trees, diamond graphs, Laksoo graphs, parasol graphs). Our motivation is to exhibit natural geometric properties of Banach spaces that prevent low-distortion embeddability of certain sequences of graphs. The study of the faithful embeddability of general metric spaces is motivated by some fundamental applications in theoretical computer science (Euclidean distortion of finite metric spaces) or in geometric group theory and topology (coarse embeddability of groups).

2:00 pm   in 347 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by rasekh2.
 Mychael Sanchez (UIUC Math)Global homotopy theoryAbstract: I’ll talk about global homotopy theory, which can be thought of as homotopy theory for spaces with simultaneous compatible actions by compact Lie groups. I’ll define and give examples of global spaces and introduce global homology theories.

2:00 pm   in 241 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by amalik10.
 Kyle Pratt (UIUC Math)A generalization of the Schur-Siegel-Smyth trace problemAbstract: Let $\alpha$ be a totally positive algebraic integer, and define its absolute trace to be $\frac{Tr(\alpha)}{\text{deg}(\alpha)}$, the trace of $\alpha$ divided by the degree of $\alpha$. Elementary considerations show that the absolute trace is always at least one, while it is conjectured that for any $\epsilon >0$, the absolute trace is at least $2-\epsilon$ with only finitely many exceptions. This is known as the Schur-Siegel-Smyth trace problem. I will discuss joint work with George Shakan and Alexandru Zaharescu in which we show that the Schur-Siegel-Smyth trace problem is a special case of a more general phenomenon.

Commutative Ring Theory Seminar
3:00 pm   in 243 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by mastroe2.
 Hal Schenck (UIUC Math)Algebra and Geometry of Wachspress surfacesAbstract: Let $P_d$ be a convex polygon with $d$ vertices. The associated Wachspress surface $W_d$ is a fundamental object in approximation theory, defined as the image of the rational map $\mathbb{P}^2 \stackrel{w_d}{\longrightarrow} \mathbb{P}^{d-1}$ determined by the Wachspress barycentric coordinates for $P_d$. We show $w_d$ is a regular map on a blowup $X_d$ of $\mathbb{P}^2$ and if $d>4$ is given by a very ample divisor on $X_d$, so has a smooth image $W_d$. We determine generators for the ideal of $W_d$, and prove that in graded lex order, the initial ideal of $I_{W_d}$ is given by a Stanley-Reisner ideal. As a consequence, we show that the associated surface is arithmetically Cohen-Macaulay, of Castelnuovo-Mumford regularity two, and determine all the graded betti numbers of $I_{W_d}$.

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 8, 2015
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Submitted by seminar.
 Anna Gilbert (University of Michigan)Recent developments in the Sparse Fourier TransformAbstract: The Discrete Fourier Transform (DFT) is a fundamental component of numerous computational techniques in signal processing and scientific computing. The most popular means of computing the DFT is the Fast Fourier Transform (FFT). However, with the emergence of big data problems, in which the size of the processed data sets can easily exceed terabytes, the "Fast" in Fast Fourier Transform is often no longer fast enough. In addition, in many big data applications it is hard to acquire a sufficient amount of data in order to compute the desired Fourier transform in the first place. The Sparse Fourier Transform (SFT) addresses the big data setting by computing a compressed Fourier transform using only a subset of the input data, in time sub-linear in the data set size. The goal of this talk is to survey these recent developments, to explain the basic techniques with examples and applications in big data, to demonstrate trade-offs in empirical performance of the algorithms, and to discuss the connection between the SFT and other techniques for massive data analysis such as streaming algorithms and compressive sensing.

Friday, October 9, 2015

Symplectic & Poisson Geometry Seminar
2:00 pm   in 143 Altgeld Hall,  Friday, October 9, 2015
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Submitted by ruiloja.
 David Li-Bland   [email] (UC Berkeley)Coherent quantization using colored surfacesAbstract: Quantization - generally speaking, the process of deforming a classical’ state space to a quantum mechanical’ one - is a problem of fundamental importance. It becomes even more challenging when one wants to quantize not just a single space in isolation, but rather to simultaneously quantize a collection of spaces in a manner which is compatible with some key structural maps between them. In fact, this is generally not possible. Nevertheless, in this talk we will describe an approach to this problem which works for a large class of spaces and structural maps which are of interest both mathematically and physically (they generalize moduli spaces of flat connections). The trick is that these spaces can be understood in terms of `colored surfaces' (which we will introduce) which are both quite visual and easy to work with. As one application, we will explain how this allows one to quantize Lie bialgebras (thus, obtaining quantum groups) and to construct certain equivariant quantizations. This talk is based on joint work with Pavol Severa.

2:00 pm   in 447 Altgeld Hall,  Friday, October 9, 2015
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Submitted by ackrmnn2.
 Chris Gartland (UIUC Math)Cannon's Conjecture and Analysis on Metric SpacesAbstract: Cannon's conjecture is one of the main open problems in geometric group theory. It states that every Gromov hyperbolic group with boundary topologically equivalent to the 2-sphere acts geometrically on hyperbolic 3-space. It turns out that this conjecture is equivalent to a uniformization problem in analysis on metric spaces - that every Gromov hyperbolic group with boundary topologically equivalent to the 2-sphere has its boundary quasisymmetrically equivalent to the 2-sphere. We will identify the major players in these two conjectures and outline a proof of their equivalence.

Algebra, Geometry and Combinatorics
4:00 pm   in 241 Altgeld Hall,  Friday, October 9, 2015
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Submitted by redavid2.
 Emmanuel Tsukerman   [email] (University of California-Berkeley)Bruhat Interval PolytopesAbstract: In this talk, I will discuss the geometry of Bruhat Interval Polytopes, polytopes which generalize the classical Permutahedron and arise from the study of the moment map on the flag variety. In the process, I will demonstrate some techniques used in the study of Coxeter groups and touch upon their applications to R-polynomials, polynomials used in defining the famous Kazhdan-Lusztig polynomials. This talk is based on joint work with Lauren Williams.

 Georgios Kydonakis (UIUC Math)Geometric properties of Higher Teichmüller SpacesAbstract: Higher Teichmüller Theory brings together different mathematical objects in describing the moduli space of fundamental group representations into a semisimple Lie group $G$. Realizing Teichmüller space as a subset of this moduli space in the case when $G=\text{PSL}\left( 2,\mathbb{R} \right)\,$, provides motivation to identify and study connected components of the representations variety, which share essential topological and geometric properties with the classical Teichmüller space. We will introduce particular examples of these components and point their special geometric significance.