Department of

# Mathematics

Seminar Calendar
for Colloquium events the year of Monday, July 17, 2017.

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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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Tuesday, January 17, 2017

4:00 pm in 245 Altgeld Hall,Tuesday, January 17, 2017

#### Gaussian Risk Models with Financial Constraints

###### Lanpeng Ji (University of Applied Sciences of Western Switzerland)

Abstract: In classical risk theory, the surplus process of an insurance company is modeled by the compound Poisson or the general compound renewal risk process. For both applied and theoretical investigations, calculation of the ruin probabilities for such models is of particular interest. In order to avoid technical issues and to allow for dependence among the claim sizes, these risk models are often approximated by the classical Brownian motion (or diffusion) (e.g., [1,2]) or the fractional Brownian motion risk model (e.g., [3,4]). Calculation of ruin probabilities and other ruin related quantities for Brownian motion and more general Gaussian risk models has been the subject of study of numerous contributions (e.g., [4-7]). This talk focuses on the most recent findings for Gaussian risk models with financial constraints such as inflation, interest and tax. In particular, three Gaussian risk models and their ruin probabilities will be discussed in detail. Finally, some future research directions on this topic will also be discussed. References: [1] Iglehart, D. L. 1969. Diffusion approximations in collective risk theory, Journal of Applied Probability 6: 285–292. [2] Grandell, J. 1991. Aspects of Risk Theory. New York: Springer. [3] Michna, Z. 1998. Self-similar processes in collective risk theory, J. Appl. Math. Stochastic Anal., 11(4): 429-448. [4] Asmussen, S. and Albrecher, H. 2010. Ruin Probabilities. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, second edition. [5] Cai, J., Gerber, H.U. and Yang, H.L. 2006. Optimal dividends in an Ornstein–Uhlenbeck type model with credit and debit interest, North American Actuarial Journal 10 (2): 94–119. [6] Debicki, K. 2002. Ruin probability for Gaussian integrated processes, Stochastic Process. Appl., 98(1): 151-174. [7] Husler, J. and Piterbarg, V.I. 2008. A limit theorem for the time of ruin in a Gaussian ruin problem, Stochastic Process. Appl., 118(11): 2014-2021. See video of talk at https://www.youtube.com/watch?v=dYUhaq2j4CQ&feature=youtu.be

Thursday, January 19, 2017

4:00 pm in 245 Altgeld Hall,Thursday, January 19, 2017

#### Risk sharing and risk aggregation via risk measures

###### Haiyan Liu (University of Waterloo)

Abstract: In this talk, we discuss two problems in risk management using the tools of risk measures. In the first part of the talk, we address the problem of risk sharing among agents using a two-parameter class of quantile-based risk measures, the so-called Range-Value-at-Risk (RVaR), as their preferences. We first establish an inequality for RVaR-based risk aggregation, showing that RVaR satisfies a special form of subadditivity. Then, the risk sharing problem is solved through explicit construction. Comonotonicity and robustness of the optimal allocations are investigated. We show that, in general, a robust optimal allocation exists if and only if none of the risk measures is a VaR. Practical implications of our main results for risk management and policy makers will be discussed. In the second part of the talk, we study the aggregation of inhomogeneous risks with a special type of model uncertainty, called dependence uncertainty, evaluated by a generic risk measure. We establish general asymptotic equivalence results for the classes of distortion risk measures and convex risk measures under different mild conditions. The results implicitly suggest that it is only reasonable to implement a coherent risk measure for the aggregation of a large number of risks with uncertainty in the dependence structure, a relevant situation for risk management practice.

Friday, January 20, 2017

4:00 pm in 245 Altgeld Hall,Friday, January 20, 2017

#### Inference for Mortality Models and Predictive Regressions

###### Liang Peng (Department of Risk Management and Insurance, Georgia State University)

Abstract: Forecasting mortality is of importance in managing longevity risks for insurance companies and pension funds. Some widely employed models are the so-called Lee-Carter model and its extensions. First we show that the proposed two-step inference procedure in Lee and Carter (1992) can not detect the true dynamics of the mortality index except when the index follows from a unit root AR(1) process. Second we propose a new method to test whether the index does follow from a unit root AR(1) model and then apply the new test to some mortality data to show that a blind application of an existing R package leads to different conclusions.

Testing for predictability of asset returns has been a long history in econometrics. Recently, based on a simple predictive regression, Kostakis, Magdalinos and Stamatogiannis (2015) proposed a Wald test derived from the IVX methodology for stock return predictability and Demetrescu (2014) showed that the local power of the standard IVX-based test could be improved in some cases when a lagged predicted variable is added to the predictive regression on purpose. Therefore an interesting question is whether a lagged predicted variable does appear in the model. Here we propose unified tests for testing the existence of a lagged predicted variable in a predictive regression and the predictability regardless of whether the predicting variable is stationary or nearly integrated or unit root. We further apply the proposed tests to some real data sets in finance.

Tuesday, January 24, 2017

4:00 pm in 245 Altgeld Hall,Tuesday, January 24, 2017

#### A New Approach for Buffering Portfolio Returns in Investment-Linked Annuities

###### Daniel Linders (Technical University of Munich)

Abstract: This paper introduces a new class of investment-linked annuity contracts. To reduce payout volatility, we gradually adjust cash flows to portfolio returns. This contrasts with standard investment-linked annuity contracts in which cash flows immediately incorporate portfolio returns. To build a realistic risk-management framework, we consider a general financial market. Our framework allows to use various non-Gaussian distributions which incorporate stylized facts about portfolio returns. Furthermore, we show how to price and hedge the liabilities of our new annuity contract.

Wednesday, January 25, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, January 25, 2017

#### Degenerate diffusions and heat kernel estimates

###### Jing Wang (J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign)

Abstract: In this talk we will look at degenerate hypoelliptic diffusion processes and the small time behaviors of their transition densities. Diffusion processes play important roles in modeling risky assets in financial mathematics and actuarial science. The small time estimates of their transition densities are particularly useful for pricing options with short maturities. In this talk we will introduce the degenerate diffusion processes that are characterized by their levels of degeneracy. The ones of weaker degeneracy -- also called strong Hörmander's type -- are closely related to sub-Riemannian geometry. An important example is the Brownian motion process on a sub-Riemannian manifold. In general, small time asymptotic estimates are available for a subelliptic heat kernel on the diagonal and out of cut-locus. In special cases such as for Brownian motions on sub-Riemannian model spaces, we can obtain explicit expressions for their transition densities (heat kernels) and hence small time asymptotic estimates, particularly on the cut-loci. In the second part of the talk, we will study the strictly degenerate case-diffusion processes that are of weak Hörmander's type. Namely the hypoellipticity is fulfilled with the help of the drift term. This type of processes are particularly interesting in financial mathematics for pricing Asian options. We obtain large deviation properties for nilpotent diffusion processes of weak Hörmander's type.

Friday, January 27, 2017

4:00 pm in 245 Altgeld Hall,Friday, January 27, 2017

#### A Marked Cox Model for IBNR Claims: Theory and Application

###### Dameng Tang (University of Waterloo)

Abstract: Incurred but not reported (IBNR) loss reserving is a very important issue for Property & Casualty (P&C) insurers. To calculate IBNR reserve, one needs to model claim arrivals and then predict IBNR claims. However, factors such as temporal dependence among claim arrivals and exposure fluctuation are often not incorporated in most of the current loss reserving models, which greatly affect the accuracy of IBNR predictions. In this talk, I will present a new modelling approach under which the claim arrival process together with the reporting delays follows a marked Cox process. The intensity function of the Cox process is governed by a hidden Markov chain. I will show that the proposed model is versatile in modeling temporal dependence, can incorporate exposure fluctuation, and can be interpreted naturally in the insurance context. The associated reported claim process and IBNR claim process remain to be a marked Cox process with easily convertible intensity function and marking distribution. The specific structure of the intensity function allows for generating discretely observed claim processes, which is critical for data fitting purposes. Closed-form expressions for both the autocorrelation function (ACF) and the distributions of the numbers of reported claims and IBNR claims are derived. I will then present a generalized expectation-maximization (EM) algorithm to fit the model to data and to estimate the model parameters. The proposed model is examined through simulation studies and is applied to a real insurance claim data set. We compare the predictive distributions of our model with those of the over-dispersed Poisson model (ODP), a stochastic model that underpins the widely used chain-ladder method. The results show that our model can yield more accurate best estimates and more realistic predictive distributions. This is joint work with Andrei Badescu and Sheldon Lin.

Monday, January 30, 2017

4:00 pm in 156 Henry Admin Bldg,Monday, January 30, 2017

#### Discounted Sums at Renewal Times

###### Daniel Dufresne (Director of the Centre for Actuarial Science, University of Melbourne)

Abstract: Actuarial models usually include discounting, to take the time value of money into account. Mathematically this has proved difficult when amounts are paid at random times, for instance in risk theory. We assume that i.i.d. amounts {C(k)} are paid at renewal times {T(k)}. Of practical interest is the distribution of Z(t), the discounted value of claims occurring over the period [0,t]. New results on how to find the distribution of Z(t) will be presented. An important tool is sampling the process {Z(t)} at an independent exponential time, which leads to explicit distributions of Z(t) in specific cases. Joint work with Zhehao Zhang.

Wednesday, February 1, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 1, 2017

#### Modular forms, quantum field theory, and algebraic topology

###### Dan Berwick-Evans (UIUC)

Abstract: Modular forms appear in a wide variety of contexts. For example, they arise in physics as partition functions of two dimensional quantum field theories and in algebraic topology as the coefficient ring of elliptic cohomology. A long-standing conjecture suggests that these two appearances of modular forms are related. After explaining the ingredients, I’ll describe some recent progress.

4:00 pm in 245 Altgeld Hall,Wednesday, February 1, 2017

#### Application of Stein's method in Spin Glass Systems

###### Tayyab Nawaz (UIUC Math)

Abstract: In 1960’s, Stein introduced a method to bound the distance between two probability distributions using a specific probability metric. For a large complex stochastic system, mean field theory is considered as a starting point to study its physical properties. In mean field theory we assume that each particle interacts with the rest of the system in a homogeneous 'average' way. In this talk, I will discuss how Stein’s method and mean field theory are used to study the energy minimization problem for spin-glass models in statistical mechanics. I will also discuss the idea of optimal Monte Carlo algorithms for solving energy minimization problem and related open problems.

Thursday, February 2, 2017

4:00 pm in 245 Altgeld Hall,Thursday, February 2, 2017

#### Random matrices, d-bar problems, and approximation theory

Abstract: Some surprising questions in analysis arise in the interconnections of the topics in the title. We will encounter zeros of the Taylor approximants of exp(z), and other analytic functions. We will consider questions of support of equilibrium charge distributions in the plane. Semi-classical analysis of d-bar problems will provide merriment along the way.

Wednesday, February 8, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 8, 2017

#### Stability and wall-crossing in algebraic geometry

###### Rebecca Tramel (UIUC)

Abstract: I will discuss two notions of stability in algebraic geometry: slope stability of vector bundles on curves, and Bridgeland stability for complexes of sheaves on smooth varieties. I will try and motivate both of these definitions with questions from algebraic geometry and from physics. I will then work through a few detailed examples to show how varying our notion of stability affects the set of stable objects, and how this relates to the geometry of the space we are studying.

Thursday, February 9, 2017

4:00 pm in 245 Altgeld Hall,Thursday, February 9, 2017

#### Tales of Elliptic fibrations

###### Mboyo Esole (Northeastern Math)

Abstract: Elliptic curves have been part of mathematics since ancient Greece and beyond. When an elliptic curve moves over a variety, it draws a fibration called a genus one fibration. The cases of surfaces have been explored by Kodaira, Neron, and others in the early 1960s. During the second string revolution, elliptic fibrations have played a central role in describing non-perturbative effects in string theory and M-theory. Ever since, ideas from physics have inspired new points of view on elliptic fibrations, providing a rich set of ideas to explore their geometry using tools from representation theory, hyperplane arrangements, intersection theory, and birational geometry. In this colloquium, I will review these ideas and present new results.

Thursday, February 16, 2017

4:00 pm in 245 Altgeld Hall,Thursday, February 16, 2017

#### Weyl law for the Volume Spectrum

###### André Neves (University of Chicago)

Abstract: The volume spectrum was introduced by Gromov in the 70’s. Recently, with Liokumovich and Marques, we proved a Weyl Law for the volume spectrum that was conjectured by Gromov. I will talk about how a better understanding of the volume spectrum would help in answering some well known questions for minimal surfaces or volume of nodal sets.

Wednesday, February 22, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, February 22, 2017

#### Topology in dimensions 1, 2 and 3

###### Mark Bell (UIUC)

Abstract: 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

4:00 pm in 245 Altgeld Hall,Thursday, February 23, 2017

#### From Picard to Rickman: Mappings in spatial quasiconformal geometry

###### Pekka Pankka (University of Helsinki)

Abstract: 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.

Wednesday, March 1, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 1, 2017

#### Quotient spaces, Lie theory and quantization

###### Ivan Contreras (UIUC)

Abstract: We encounter quotient spaces everywhere in mathematics: circles, cohomology groups, moduli spaces. And sometimes physicists come up with interpretations of such spaces in terms of the symmetries of a given theory. In this talk I will explain how a 2 dimensional topological field theory, called the Poisson sigma model, produce interesting symplectic quotient spaces and its quantization produce deformations of Poisson brackets.

4:00 pm in 245 Altgeld Hall,Wednesday, March 1, 2017

#### Convexity and curvature in space-time geometry

###### William Karr (UIUC Math)

Abstract: A space-time is said to satisfy $\mathcal{R} \geq K$ if the sectional curvatures of spacelike planes are bounded below by $K$ and the sectional curvatures of timelike planes are bounded above by $K$. Similarly, one can define $\mathcal{R} \leq K$ by reversing the inequalities. These conditions naturally generalize the notion of curvature bounds for Riemannian manifolds to the Lorentzian setting. We describe how these conditions can be used to construct two types of convex functions. We then describe two geometric consequences of space-times supporting these functions. One result establishes geodesic connectedness for a class of space-times satisfying $\mathcal{R} \geq 0$. Another result rules out submanifolds associated with black holes and wormholes in certain domains of space-times satisfying $\mathcal{R} \leq 0$. This is joint work with Stephanie Alexander.

Wednesday, March 8, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 8, 2017

#### What is the mollification of the Riemann zeta-function?

###### Nicolas Robles (UIUC)

Abstract: We explain how to compute mean value integrals of the Riemann zeta-function involving a special type of Dirichlet polynomial called a mollifier. This process will allows us to compute an explicit proportion of the zeros of the Riemann zeta-function on the critical line, namely that more than 2/5 of them satisfy the Riemann hypothesis.

Thursday, March 16, 2017

4:00 pm in 245 Altgeld Hall,Thursday, March 16, 2017

#### The Topological Closure of Algebraic and Semi-Algebraic Flows on Complex and Real Tori

###### Sergei Starchenko (Notre Dame)

Abstract: Let $A$ be a complex abelian variety and $\pi\colon \mathbb{C}^n\to A$ be the covering map. In this talk we consider the topological closure $\pi(X)$ of an algebraic subvariety $X$ of $\mathbb{C}^n$ and describe it in terms of finitely many algebraic families of cosets of real subtori. We also obtain a similar description when $A$ is a real torus and $X$ is a semi-algebraic subset of $\mathbb{R}^n$. This is joint work with Y. Peterzil.

Monday, March 27, 2017

2:00 pm in 245 Altgeld Hall,Monday, March 27, 2017

#### A Mathematical View of Biology and Diversification

###### Vanessa Rivera-Quiñones (Illinois Math)

Abstract: Have you ever wondered about the meaning of the phrase "survival of the fittest"? To an evolutionary biologist, fitness simply means reproductive success and reflects how well an organism is adapted to its environment. How systems adapt over time has been a central question in Biology and other Life-Sciences. While I will focus on the theory of Adaptive Dynamics, there are many areas of mathematics that have contributed to our understanding of adaptation. In this talk, I will give an overview of how we can use mathematical models to understand adaptation as an evolutionary process and its relationship to creating and preserving diversity. If time permits, I will also address the connections between this theory and my own research in disease modeling.

Wednesday, March 29, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, March 29, 2017

#### Apollonian Circle Packings and Beyond: Number Theory, Graph Theory and Geometric Statistics

###### Xin Zhang (UIUC)

Abstract: An Apollonian circle packings (ACP) is an ancient Greek construction obtained by repeatedly inscribing circles to an original configuration of three mutually tangent circles. In the last decade, the surprisingly rich structure of ACP has attracted experts from different fields: number theory, graph theory, homogeneous dynamics, to name a few. In this talk, I’ll survey questions and the progress on this topic and related fields.

Thursday, March 30, 2017

4:00 pm in 245 Altgeld Hall,Thursday, March 30, 2017

#### Projections and Curves in Infinite-Dimensional Banach Spaces

###### Bobby Wilson (MIT and MSRI)

Abstract: In this talk, we will discuss the measure theoretic principles of orthogonal projections including the classical Besicovitch-Federer projection theorem. The Besicovitch-Federer projection theorem offers a characterization of rectifiability of one-dimensional sets in R^d by the size of their projections to lines. We will focus on the validity of analogues to the Besicovitch-Federer projection theorem with respect to such sets in general Banach spaces. In particular, we will show that the projection theorem is false when the Banach space is infinite-dimensional and discuss some related questions. This is joint work with Marianna Csornyei and David Bate.

Wednesday, April 5, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 5, 2017

#### Vertex algebras, chiral algebras, and factorization algebras

###### Emily Cliff (UIUC)

Abstract: The definition of a vertex algebra was formulated by Borcherds in the 1980s to solve algebraic problems, but these objects turn out to have important applications in mathematical physics, especially related to models of 2d conformal field theory. In the 1990s, Beilinson and Drinfeld gave geometric formulations of the definition, which they called chiral algebras and factorization algebras. These different approaches each have advantages and disadvantages: for example, the definition of a vertex algebra is more concrete and has so far been better studied; on the other hand, the geometric approach of chiral algebras and factorization algebras allows for transfer of knowledge between the fields of geometry, physics, and representation theory, and furthermore admits natural generalizations to higher dimensions. In this talk we will introduce all three of these objects; then we will discuss the relationships between them, especially focusing on how information from any one approach can lead to new understanding in the others.

Thursday, April 6, 2017

4:00 pm in 245 Altgeld Hall,Thursday, April 6, 2017

#### On the transport property of Gaussian measures under Hamiltonian PDE dynamics

Abstract: In probability theory, the transport property of Gaussian measures have attracted wide attention since the seminal work of Cameron and Martin '44. In this talk, we discuss recent development on the study of the transport property of Gaussian measures on spaces of functions under nonlinear Hamiltonian PDE dynamics. As an example, we will discuss the case for the 2-d cubic nonlinear wave equation, for which we introduce a simultaneous renormalization of the energy functional and its time derivative to study the transport property of Gaussian measures on Sobolev spaces. This talk is based on a joint work with Nikolay Tzvetkov (Université de Cergy-Pontoise).

Tuesday, April 11, 2017

4:00 pm in 245 Altgeld Hall,Tuesday, April 11, 2017

#### Harmonic analysis techniques in several complex variables

###### Loredana Lanzani (Syracuse University)

Abstract: This talk concerns the application of relatively classical tools from real harmonic analysis (namely, the $T(1)$-theorem for spaces of homogenous type) to the novel context of several complex variables. Specifically, I will present recent joint work with E. M. Stein on the extension to higher dimension of Calderón's and Coifman-McIntosh-Meyer's seminal results about the Cauchy integral for a Lipschitz planar curve (interpreted as the boundary of a Lipschitz domain $D\subset{\mathbb C}$). From the point of view of complex analysis, a fundamental feature of the 1-dimensional Cauchy kernel $H(w, z) = \tfrac{1}{2\pi i}(w-z)^{-1}dw$ is that it is holomorphic as a function of $z\in D$. In great contrast with the one-dimensional theory, in higher dimension there is no obvious holomorphic analogue of $H(w, z)$. This is because geometric obstructions arise (the Levi problem), which in dimension one are irrelevant. A good candidate kernel for the higher dimensional setting was first identified by Jean Leray in the context of a $C^\infty$-smooth, convex domain $D$: while these conditions on $D$ can be relaxed a bit, if the domain is less than $C^2$-smooth (never mind Lipschitz!) Leray's construction becomes conceptually problematic. In this talk I will present (i) the construction of the Cauchy-Leray kernel and (ii) the $L^p(bD)$-boundedness of the induced singular integral operator under the weakest currently known assumptions on the domain's regularity -- in the case of a planar domain these are akin to Lipschitz boundary, but in our higher-dimensional context the assumptions we make are in fact optimal. The proofs rely in a fundamental way on a suitably adapted version of the so-called "$T(1)$-theorem technique" from real harmonic analysis. Time permitting, I will describe applications of this work to complex function theory -- specifically, to the Szego and Bergman projections (that is, the orthogonal projections of $L^2$ onto, respectively, the Hardy and Bergman spaces of holomorphic functions).

Wednesday, April 12, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 12, 2017

#### First order logic and Sub-riemannian spheres.

###### Erik Walsberg (UIUC)

Abstract: I will discuss a connection between sub-riemannian geometry and first order model theory. Researchers in sub-riemannian geometry have essentially been working on the following: are sub-riemannian spheres definable in an o-minimal expansion of the ordered field of real numbers? (O-minimality is an important and popular topic in model theory developed in large part by UIUC's own Lou van den Dries). It also seems that some model theorists have been trying to construct the kind of structure that the geometers are looking for. As far as I can tell neither side was really aware of what the other was doing until now. I will try to explain some of this. No knowledge of logic or sub-riemannian geometry is necessary.

Wednesday, April 19, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, April 19, 2017

#### An introduction to enumerative geometry

###### Yun Shi (UIUC Math)

Abstract: One important question in enumerative geometry concerns how many curves there are on a Calabi-Yau 3-fold. In this talk, I will present one of the approaches to the classical problem: there are 27 lines on a smooth cubic surface. Motivated by this approach, we will discuss the modern set-up to answer the curve counting questions, in particular its applications to Donaldson-Thomas theory.

Thursday, April 20, 2017

4:00 pm in 245 Altgeld Hall,Thursday, April 20, 2017

#### Tarski numbers

###### Mark Sapir (Centennial Professor, Vanderbilt University, and George A. Miller Visiting Professor, Univ. of Illinois)

Abstract: It is known since Hausdorff, Banach and Tarski that one can decompose a 2-sphere into 4 pieces, move the pieces using rotations of the sphere, and obtain two spheres of the same radius (assuming the Axiom of Choice). Thus a sphere with the group of rotations acting on it has a paradoxical decomposition with 4 pieces. In general if we have a group G acting on a set X, then the Tarski number of X is the minimal number of pieces in a paradoxical decomposition of X. For example, if G acts on itself by left multiplication, then we can talk about the Tarski number of G. I will show how to use Golod-Shafarevich groups to prove that the set of possible Tarski numbers of groups is infinite. I will also show how to use l_2-Betti numbers of groups and cost of group actions to construct groups with Tarski numbers 5 and 6. Note that 4, 5 and 6 are the only numbers that are currently known to be Tarski numbers of groups. This is a joint work with Gili Golan and Mikhail Ershov.

Tuesday, April 25, 2017

4:00 pm in 314 Altgeld Hall,Tuesday, April 25, 2017

#### Cobordisms: old and new

###### Ulrike Tillmann (Oxford University)

Abstract: Cobordims have played an important part in the classification of manifolds since their invention in the 1950s. In a different way, they are fundamental to the axiomatic approach to Topological Quantum Field Theory. In this colloquium style talk I will explain how recent results have shed new light on both of them.

The Tondeur Lectures in Mathematics will be held April 25-27, 2017. A reception will be held following the first lecture from 5-6 pm April 25 in 239 Altgeld Hall.

Wednesday, April 26, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, April 26, 2017

#### Merit Program for Emerging Scholars

###### Jennifer McNeilly (UIUC)

Abstract: The Merit Program at the University of Illinois has helped with the retention and recruitment of underrepresented students in STEM fields for nearly three decades. With this talk, I will briefly review the history of the program and describe how it is structured in our department. I will also describe the teaching methods used (based on Dr. Uri Treisman’s collaborative learning model) and share some examples/data to demonstrate the program’s success. The goals will be to both introduce the Merit Program to those who are unfamiliar with it and also share a few teaching and TA training ideas which could be useful in a variety of settings.

4:00 pm in 245 Altgeld Hall,Wednesday, April 26, 2017

#### Classifying spaces of bordism categories and a filtration of Thom's theory

###### Ulrike Tillmann (Oxford University)

Abstract: We describe a refinement of a theorem with Galatius, Madsen and Weiss which describes the classifying space of bordism categories. In particular this can be interpreted to give evidence for the cobordism hypothesis for invertible TQFTs.

The Tondeur Lectures in Mathematics will be held April 25-27, 2017. A reception will be held following the first lecture from 5-6 pm April 25 in 239 Altgeld Hall.

Thursday, April 27, 2017

4:00 pm in 245 Altgeld Hall,Thursday, April 27, 2017

###### Ulrike Tillmann (Oxford University)

Abstract: Manifolds give rise to interesting operads, and in particular TQFTs define algebras over these operads. In the case of Atiyah's 1+1 dimensional theories these algebras are well-known to correspond to certain algebras. Surprisingly, independent of the dimension of the underlying manifolds, in the topologically enriched setting the manifold operads detect infinite loop spaces. We will report on joint work with Basterra, Bobkova, Ponto, Yeakel.

The Tondeur Lectures in Mathematics will be held April 25-27, 2017. A reception will be held following the first lecture from 5-6 pm April 25 in 239 Altgeld Hall.

Wednesday, May 3, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, May 3, 2017

#### Quantitative Mostow Rigidity: Relating volume to topology for hyperbolic 3-manifolds

###### Rosemary Guzman (UIUC)

Abstract: A celebrated result of Mostow states that if M, N are two closed, con- nected, orientable, hyperbolic n-manifolds which are homotopy equivalent in dimensions $n\geq 3$, then M, N are equivalent up to isometry. This unique geometric-topological relationship has been the framework for many important results in the field, including notable results providing lower bounds on the volume of M, and results relating volume to homology (Culler-Shalen). In this talk, we will focus on the case where the fundamental group of M has a property, $k-$free, for $k\geq5$, and discuss current work toward an improvement on the volume bound from the current known bound of 3.44 which holds for $k\geq 4$. This is joint work with Peter Shalen.

Thursday, May 4, 2017

4:00 pm in 245 Altgeld Hall,Thursday, May 4, 2017

#### The L^2 metric on Hitchin’s moduli space

###### Rafe Mazzeo (Stanford)

Abstract: The much-studied moduli space of solutions to Hitchin’s equations on a Riemann surface carries a natural complete Weil-Petersson type metric. The large-scale structure of this metric is only now being revealed, first through an ambitious set of physics conjectures by Gaiotto-Neitzke-Moore, and now through techniques of geometric analysis. I will discuss this whole picture and report on recent work with Swoboda-Weiss-Witt.

Thursday, July 20, 2017

4:00 pm in 114 David Kinley Hall (NOTE SPECIAL LOCATION),Thursday, July 20, 2017

#### Moment Maps of Toric Varieties, Linear Precision, and Maximum Likelihood Degree One

###### David A. Cox (Department of Mathematics and Statistics, Amherst College)

Abstract: The quotient construction of the toric variety of a lattice polytope gives a canonically defined moment map. Other moment maps come from projective embeddings of the toric variety that use the ample line bundle determined by the polytope. It is natural to ask if the quotient moment map is one of these projective moment maps. My lecture will explain how this relates to linear precision in geometric modeling and and maximum likelihood degree one in algebraic statistics. This is joint work with Patrick Clarke of Drexel University.

Thursday, August 31, 2017

4:00 pm in 245 Altgeld Hall,Thursday, August 31, 2017

#### Symplectic non-squeezing for the cubic nonlinear Schrodinger equation on the plane

###### Monica Visan (UCLA)

Abstract: A famous theorem of Gromov states that a finite dimensional Hamiltonian flow cannot squeeze a ball inside a cylinder of lesser radius, despite the fact that the ball has finite volume and the cylinder has infinite volume. We will discuss an infinite-dimensional analogue of Gromov's result, in infinite volume. Specifically, we prove that the flow of the cubic NLS in two dimensions cannot squeeze a ball in $L^2$ into a cylinder of lesser radius. This is joint work with R. Killip and X. Zhang.

Wednesday, September 6, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

#### Truncation in Generalized Series Fields

###### Santiago Camacho (Illinois Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

4:00 pm in 245 Altgeld Hall,Wednesday, September 6, 2017

#### Truncation in Generalized Series Fields

###### Santiago Camacho (UIUC Math)

Abstract: Taylor polynomials are very useful for approximating analytic functions, nevertheless there is increasing interest in understanding so-called analyzable functions that are not necessarily analytic. For this reason fields of generalized series (Hahn fields) that extend Laurent series have been studied. A natural analogue of Taylor or Laurent polynomials in these series fields are truncated series. We explore some of the stability properties of truncation closed subsets of Hahn Fields.

Thursday, September 7, 2017

4:00 pm in 245 Altgeld Hall,Thursday, September 7, 2017

#### Random groups and surfaces

###### Moon Duchin (Tufts)

Abstract: I'll survey some of the beautiful history of the study of random objects in geometry, topology, and group theory. The focus will be the exchanges between work on random groups and work on random surfaces, including some very recent results and current research topics.

Wednesday, September 13, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, September 13, 2017

#### Panel: Writing Grant Applications

###### Philipp Hieronymi, Vera Hur, Jennifer Mcneilly, Alexander Yong (UIUC)

Abstract: Postdocs, lecturers and faculty in general must face oftentimes the task of writing applications for grants: NSF, travel grants, teaching reduction, etc. The idea of this panel is to bring together some members of our faculty, with recognized success in grant applications, to share their thoughts on the subject and to answer questions from the audience.

Thursday, September 14, 2017

4:00 pm in 245 Altgeld Hall,Thursday, September 14, 2017

#### Probabilistic and combinatorial methods in the study of prime gaps

###### Kevin Ford (Illinois)

Abstract: We will describe how new bounds for the largest gaps between consecutive primes have utilized tools from several different areas, including number theory (efficient prime detecting sieves), probability (randomized congruence system coverings, concentration arguments) and probabilistic combinatorics (hypergraph covering). In particular, we will outline the recent breakthroughs of the speaker together with Ben Green, Sergei Konyain, James Maynard and Terence Tao. We will also describe new work with Konyagin, Maynard, Carl Pomerance and Tao which provides new bounds on consecutive composite values of integers in other sequences, e.g. polynomial sequences.

Thursday, September 21, 2017

4:00 pm in 245 Altgeld Hall,Thursday, September 21, 2017

#### The Man Who Knew Infinity: the Movie, the Man, and the Mathematics

###### George Andrews (Penn State)

Abstract: In the spring of 2016, the motion picture, The Man Who Knew Infinity, was released. It is now available on DVD. The movie tells the life story of the Indian genius, Ramanujan. In this talk, I hope to start with the trailer from the movie. Then I shall provide a brief discussion of Ramanujan's life with a glimpse of the mathematics contained in his celebrated Lost Notebook (of which Bruce Berndt and I have just concluded preparing the fifth and final volume explicating the many assertion therein). The bulk of the talk will consider the path from the Rogers-Ramanujan identities to current open problems and how computer algebra assists in their study.

Wednesday, September 27, 2017

3:00 pm in 243 Altgeld Hall,Wednesday, September 27, 2017

#### Applications of Mining Public Genome Data to Recover Statistical Trends using Geometric Combinatorics

###### Ruth Davidson (UIUC)

Abstract: Websites such as TreeBASE.org and datadryad.org provide public access to a wealth of genomic data released with peer-reviewed biological publications. Phylogenomics-the recovery of the common evolutionary history of a group of taxa from short gene samples recovered from long genomes-is a basic area of research that gives rise to many quantitative methods for mining data for evolutionary signals. In turn, myriad fields such as ecology, medicine, and linguistics consume these methods; thus improved methods have very broad scientific impact. We present a publication (joint work with MaLyn Lawhorn, Joseph Rusinko, and Noah Weber) that provides a baseline framework, built on geometric combinatorics, for studying statistical trends in genomic data. Further, we will outline future research directions that will (1) build on this framework to inform the development of new theory and methods for model-testing, and (2) improve the understanding of trends in phylogenomic data in the systematic biology, computer science, statistics, and mathematics communities.

Thursday, October 5, 2017

4:00 pm in 245 Altgeld Hall,Thursday, October 5, 2017

#### TBA

###### Marco Gualtieri (Toronto)

Tuesday, October 10, 2017

4:00 pm in 314 Altgeld Hall,Tuesday, October 10, 2017

#### TBA

###### Alexander Kechris (Caltech)

Abstract: The Trjitzinsky Memorial Lectures will be held October 10-12, 2017. A reception will follow the first lecture on October 10 from 5-6 pm in 239 Altgeld Hall.

Wednesday, October 11, 2017

4:00 pm in 245 Altgeld Hall,Wednesday, October 11, 2017

#### TBA

###### Alexander Kechris (Caltech)

Abstract: The Trjitzinsky Memorial Lectures will be held October 10-12, 2017. A reception will follow the first lecture on October 10 from 5-6 pm in 239 Altgeld Hall.

Thursday, October 12, 2017

4:00 pm in 245 Altgeld Hall,Thursday, October 12, 2017

#### TBA

###### Alexander Kechris (Caltech)

Abstract: The Trjitzinsky Memorial Lectures will be held October 10-12, 2017. A reception will follow the first lecture on October 10 from 5-6 pm in 239 Altgeld Hall.

Thursday, October 19, 2017

4:00 pm in 245 Altgeld Hall,Thursday, October 19, 2017

#### To Be Announced

###### Gloria Mari Beffa (University of Wisconsin-Madison)

Thursday, October 26, 2017

4:00 pm in 245 Altgeld Hall,Thursday, October 26, 2017

#### TBA

###### Emmy Murphy (Northwestern)

Thursday, November 9, 2017

4:00 pm in 245 Altgeld Hall,Thursday, November 9, 2017

#### To Be Announced

###### Emily Riehl (Johns Hopkins University)

Thursday, November 16, 2017

4:00 pm in 245 Altgeld Hall,Thursday, November 16, 2017

#### TBA

###### James Maynard (Institute For Advanced Study, Princeton)

Thursday, November 30, 2017

4:00 pm in 245 Altgeld Hall,Thursday, November 30, 2017

#### TBA

###### Jasmine Foo (Minnesota)

Thursday, December 7, 2017

4:00 pm in 245 Altgeld Hall,Thursday, December 7, 2017