Department of

Mathematics


Seminar Calendar
for events the day of Tuesday, April 16, 2019.

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Tuesday, April 16, 2019

11:00 am in 345 Altgeld Hall,Tuesday, April 16, 2019

Iterated K-theory of the integers and higher Lichtenbaum-Quillen conjectures

Gabe Angelini-Knoll (Michigan State University)

Abstract: The Hurewicz image of the alpha family in the algebraic K-theory of the integers is know to correspond to special values of the Riemann zeta function, by work of Adams and Quillen. Lichtenbaum and Quillen conjectured that, more generally, there should be a relationship between special values of Dedekind zeta functions and algebraic K-theory. These conjectures have now largely been proven by work of Voevodsky and Rost. The red-shift conjectures of Ausoni-Rognes generalize the Lichtenbaum-Quillen conjecture to higher chromatic heights in a precise sense. In that same spirit, I conjecture that the n-th Greek letter family is detected in the Hurewicz image of the n-th iteration of algebraic K-theory of the integers. In my talk, I will sketch a proof of this conjecture in the case n=2 using the theory of trace methods. Specifically, I prove that the beta family is detected in the Hurewicz image of iterated algebraic K-theory of the integers. This is a higher chromatic height analogue of the result of Adams and Quillen. Consequently, by work of Behrens, Laures, and Larson iterated algebraic K-theory of the integers detects explicit information about certain modular forms.

1:00 pm in 345 Altgeld Hall,Tuesday, April 16, 2019

Positive model theory and sober spaces

Levon Haykazyan (University of Waterloo)

Abstract: I will talk about positive model theory (also known as coherent logic) where formulas are not closed under negation. This setting is in fact more general that full first-order logic, since negation can be expressed by changing the language. The result is that we can have as much negation as necessary, however no extra negation is forced by the framework.
  We can associate to a positive theory a natural spaces of types, which will no longer be Hausdorff, but (quasi-)compact and sober. I will show that these spaces play the role of the Stone spaces in the full first-order logic. In particular I will show how classical results (due to Vaught) connecting the structure of countable models to Stone spaces carry over to the positive setting, provided we find the appropriate formulations of topological properties for non-Hausdorff spaces.

2:00 pm in 345 Altgeld Hall,Tuesday, April 16, 2019

Large deviations for quasilinear parabolic stochastic partial differential equations

Rangrang Zhang (Beijing Institute of Technology and University of Tennessee)

Abstract: In this talk I will present some recent results on large deviations for quasilinear parabolic stochastic partial differential equations. More precisely, I will talk about Freidlin-Wentzell type large deviations for quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are not necessarily locally monotone. Our proof is based on the weak convergence approach.

2:00 pm in 243 Altgeld Hall,Tuesday, April 16, 2019

Monochromatic connected matchings, paths and cycles in 2-edge-colored multipartite graphs

Xujun Liu (Illinois Math)

Abstract: We solve four similar problems: For every fixed $s$ and large $n$, we describe all values of $n_1,\ldots,n_s$ such that for every $2$-edge-coloring of the complete $s$-partite graph $K_{n_1,\ldots,n_s}$ there exists a monochromatic
(i) cycle $C_{2n}$ with $2n$ vertices,
(ii) cycle $C_{\geq 2n}$ with at least $2n$ vertices,
(iii) path $P_{2n}$ with $2n$ vertices, and
(iv) path $P_{2n+1}$ with $2n+1$ vertices.

This implies a generalization of the conjecture by Gyárfás, Ruszinkó, Sárközy and Szemerédi that for every $2$-edge-coloring of the complete $3$-partite graph $K_{n,n,n}$ there is a monochromatic path $P_{2n+1}$. An important tool is our recent stability theorem on monochromatic connected matchings (A matching $M$ in $G$ is connected if all the edges of $M$ are in the same component of $G$). We will also talk about exact Ramsey-type bounds on the sizes of monochromatic connected matchings in $2$-colored multipartite graphs. Joint work with József Balogh, Alexandr Kostochka and Mikhail Lavrov.

2:00 pm in 347 Altgeld Hall,Tuesday, April 16, 2019

Testing families of analytic discs

Luca Baracco (University of Padova, Italy)

Abstract: It is a well-known fact in the theory of several complex variables that a function is holomorphic if and only if it is holomorphic in each variable separately. This result goes back to Hartogs. It is natural to consider a boundary version of Hartogs’ theorem. The general problem is to take a boundary function and ask if holomorphic extensions on some families of complex curves are enough to guarantee an extension which is holomorphic in all variables simultaneously. We will talk about the known results on the subject and show some new results obtained in collaboration with M. Fassina and S. Pinton for the special case of the unit ball in ${\mathbb C}^n$.

3:00 pm in 245 Altgeld Hall,Tuesday, April 16, 2019

An Integrated Approach to Measuring Asset and Liability Risks in Financial Institutions

George Zanjani (Professor of Finance and the Frank Park Samford Chair of Insurance, University of Alabama)

Abstract: Risk measurement models for financial institutions typically focus on the net portfolio position and thus ignore distinctions between 1) assets and liabilities and 2) uncollateralized and collateralized liabilities. However, these distinctions are economically important. Liability risks affect the total amount of claims on the institution, while asset risks affect the amount available for claimants. Collateralization also affects the amounts recovered by different classes of claimants. We analyze a model of a financial institution with risky assets and liabilities, with potentially varying levels of collateralization across liabilities, showing that correct economic risk capital allocation requires complete segregation of asset, uncollateralized liability, and collateralized liability risks, with different risk measures for each. Our numerical analyses suggest that the conventional approach frequently yields over-investment in risky assets.

Bio: George Zanjani is Professor of Finance and the Frank Park Samford Chair of Insurance at the University of Alabama. Previously, he served as the inaugural holder of the AAMGA Distinguished Chair in Risk Management and Insurance and an associate professor in the RMI Department of Georgia State University. Prior to his career in academia, he served as an economist at the Federal Reserve Bank of New York (2000–2008) specializing in policy work relating to insurance issues in the broader financial system. During his tenure at the Bank, he served on working groups formed by the Committee on the Global Financial System and the Presidential Working Group on Financial Markets. He also worked as an actuary at Fireman’s Fund Insurance Companies (1990–1994), focusing on commercial insurance pricing and heading the firm’s workers’ compensation actuarial unit in 1994.

Dr. Zanjani's published or forthcoming work includes insurance papers in the American Economic Review, Insurance: Mathematics and Economics, the Journal of Financial Economics, the Journal of Public Economics, the Journal of Risk and Insurance, Management Science, and the North American Actuarial Journal. He has served on working groups formed by the Committee on the Global Financial System (on global savings and asset allocation) and the Presidential Working Group on Financial Markets (terrorism insurance).

Dr. Zanjani is an Associate of the Casualty Actuarial Society. He earned his A.B./B.S. in Economics and Biology from Stanford University and holds a Ph.D. in Economics from the University of Chicago. He served as the President of both the American Risk and Insurance Association and the Risk Theory Society.

3:00 pm in 243 Altgeld Hall,Tuesday, April 16, 2019

Stokes decompositions and wild monodromy

Philip Boalch (Orsay)

Abstract: Just like a Hodge structure can be described equivalently in terms of the Hodge filtration or the Hodge decomposition, a Stokes structure has several equivalent descriptions. The best known are the Stokes filtrations and the Stokes local systems (or wild monodromy representations). In this talk I will explain how to formalise the notion of {\em Stokes decompositions}, to intermediate between them. This is part of an attempt (the Lax project) to understand the bestiary of complete hyperkahler manifolds that occur as moduli spaces of algebraic Higgs bundles on the affine line.

4:00 pm in 243 Altgeld Hall,Tuesday, April 16, 2019

Visualizing nonlinear dynamical systems like SIR

George K Francis   [email] (University of Illinois at Urbana–Champaign)

Abstract: There is no new presentation this week. But ...

.. for those of you who are interested in programming real-time interactive computer animations of non-linear dynamical systems, like the SIR system we saw last week in Heejeon's seminar on Koopman's theory, I will be there to introduce you to the issues and and problems involved. Recall that the SIR models the epidemiological progress of three populations: Susceptible, Infected, Recovered from the disease (thinks of measles or mumps).

In the first of (possibly) two such workshops I will treat the "continuous" case, which involves some (elementary) integration of 3D differential systems and their steady-states (attractors). In the (tentative) second workshop I will treat the "discrete" case, animating cellular automata, since both are relevant to the SIR model.

5:00 pm in TBA,Tuesday, April 16, 2019