Seminar Calendar
for Mathematics Colloquium events the year of Friday, April 21, 2017.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 17, 2017

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 17, 2017
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Lanpeng Ji (University of Applied Sciences of Western Switzerland)
Gaussian Risk Models with Financial Constraints
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Thursday, January 19, 2017
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Haiyan Liu (University of Waterloo)
Risk sharing and risk aggregation via risk measures
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Friday, January 20, 2017
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Liang Peng (Department of Risk Management and Insurance, Georgia State University)
Inference for Mortality Models and Predictive Regressions
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Tuesday, January 24, 2017
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Daniel Linders (Technical University of Munich)
A New Approach for Buffering Portfolio Returns in Investment-Linked Annuities
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Wednesday, January 25, 2017
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Jing Wang (J.L. Doob Research Assistant Professor, University of Illinois at Urbana-Champaign)
Degenerate diffusions and heat kernel estimates
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 Hörmander'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 Hörmander'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 Hörmander's type.

Friday, January 27, 2017

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 245 Altgeld Hall,  Friday, January 27, 2017
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Dameng Tang (University of Waterloo)
A Marked Cox Model for IBNR Claims: Theory and Application
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

Mathematics Colloquium - Special Lecture 2016-2017
4:00 pm   in 156 Henry Admin Bldg,  Monday, January 30, 2017
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Daniel Dufresne (Director of the Centre for Actuarial Science, University of Melbourne)
Discounted Sums at Renewal Times
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.

Thursday, February 2, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 2, 2017
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Ken McLaughlin (Colorado State)
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.

Thursday, February 9, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 9, 2017
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Mboyo Esole (Northeastern Math)
Tales of Elliptic fibrations
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

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 16, 2017
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André Neves (University of Chicago)
Weyl law for the Volume Spectrum
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.

Thursday, February 23, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, February 23, 2017
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Pekka Pankka (University of Helsinki)
From Picard to Rickman: Mappings in spatial quasiconformal geometry
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.

Thursday, March 16, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 16, 2017
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Sergei Starchenko (Notre Dame)
The Topological Closure of Algebraic and Semi-Algebraic Flows on Complex and Real Tori
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.

Thursday, March 30, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, March 30, 2017
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Bobby Wilson (MIT and MSRI)
Projections and Curves in Infinite-Dimensional Banach Spaces
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.

Thursday, April 6, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 6, 2017
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Tadahiro Oh (Edinburgh)
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

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Tuesday, April 11, 2017
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Loredana Lanzani (Syracuse University)
Harmonic analysis techniques in several complex variables
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).

Thursday, April 20, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, April 20, 2017
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Mark Sapir (Centennial Professor, Vanderbilt University, and George A. Miller Visiting Professor, Univ. of Illinois)
Tarski numbers
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

Mathematics Colloquium: Tondeur Lectures in Mathematics
4:00 pm   in 314 Altgeld Hall,  Tuesday, April 25, 2017
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Ulrike Tillmann (Oxford University)
Cobordisms: old and new
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

Mathematics Colloquium: Tondeur Lectures in Mathematics
4:00 pm   in 245 Altgeld Hall,  Wednesday, April 26, 2017
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Ulrike Tillmann (Oxford University)
Classifying spaces of bordism categories and a filtration of Thom's theory
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

Mathematics Colloquium: Tondeur Lectures in Mathematics
4:00 pm   in 245 Altgeld Hall,  Thursday, April 27, 2017
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Ulrike Tillmann (Oxford University)
Operads from TQFTs
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.

Thursday, May 4, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, May 4, 2017
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Rafe Mazzeo (Stanford)
The L^2 metric on Hitchin’s moduli space
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, September 7, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, September 7, 2017
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Moon Duchin (Tufts)
TBA

Thursday, September 21, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, September 21, 2017
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George Andrews (Penn State)
TBA

Thursday, October 5, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 5, 2017
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Marco Gualtieri (Toronto)
TBA

Tuesday, October 10, 2017

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in 314 Altgeld Hall,  Tuesday, October 10, 2017
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Alexander Kechris (Caltech)
TBA
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

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in 245 Altgeld Hall,  Wednesday, October 11, 2017
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Alexander Kechris (Caltech)
TBA
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

Mathematics Colloquium: Trjitzinsky Memorial Lectures
4:00 pm   in 245 Altgeld Hall,  Thursday, October 12, 2017
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Alexander Kechris (Caltech)
TBA
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 26, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, October 26, 2017
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Emmy Murphy (Northwestern)
TBA

Thursday, November 30, 2017

Mathematics Colloquium
4:00 pm   in 245 Altgeld Hall,  Thursday, November 30, 2017
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Jasmine Foo (Minnesota)
TBA