Department of

Mathematics


Seminar Calendar
for events the day of Monday, September 17, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 17, 2018

3:00 pm in 243 Altgeld Hall,Monday, September 17, 2018

Pre-Calabi-Yau structures and moduli of representations

Wai-kit Yeung (Indiana University)

Abstract: Pre-Calabi-Yau structures are certain structures on associative algebras introduced by Kontsevich and Vlassopoulos. This incorporates as special cases many other algebraic structures of diverse origins. Elementary examples include double Poisson algebras introduced by Van den Bergh, as well as infinitesimal bialgebras studied by Aguiar. Other examples also arise from symplectic topology as well as from string topology, whose relation with topological conformal field theory can be formulated in terms of pre-Calabi-Yau structures. In this talk, we will define pre-Calabi-Yau structures, and study it in the context of noncommutative algebraic geometry. In particular, we show that Calabi-Yau structures, introduced by Ginzburg and Kontsevich-Vlassopoulos, can be viewed as noncommutative analogue of symplectic structures. Pushing this analogy, one can show that pre-Calabi-Yau structures are noncommutative analogue of Poisson structures. As a result, we indicate how a pre-Calabi-Yau structure on an algebra induces a (shifted) Poisson structure on the moduli space of representations of that algebra.

3:00 pm in 345 Altgeld Hall,Monday, September 17, 2018

Trichotomies in Cohomology and Integrable Systems

Matej Penciak (UIUC Math)

Abstract: In integrable systems, it is often the case that solutions can be divided into 3 classes: rational, trigonometric, and elliptic. This trichotomy is also apparent in the 3 classes of cohomology theories admitting chern classes: (singular) cohomology, K-theory, and elliptic cohomology. In this talk I will describe work by Ginzburg, Kapranov, and Vasserot (and subsequently, many others) synthesizing these two phenomena.

4:00 pm in 239 Altgeld Hall,Monday, September 17, 2018

Building your own Möbius kaleidocycles

Eliot Fried (Mathematics, Mechanics, and Materials Unit, Okinawa Institute of Science and Technology Graduate University)

Abstract: Kaleidocycles are internally mobile ring linkages consisting of tetrahedra which are connected by revolute hinges. Instead of the classical, very popular, kaleidocycles with even numbers (usually six, sometimes eight) of elements, we will build kaleidocycles with seven or nine elements and several different surface designs. Moreover, we will learn that it is possible to construct kaleidocycles with any number of elements greater than or equal to six. These new kaleidocycles have two novel properties: they have only a single degree of freedom and they have the topology of a Möbius band.

4:00 pm in 245 Altgeld Hall,Monday, September 17, 2018

Primes, Permutations, Polynomials and Poisson

Kevin Ford   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: We explore connections between the distribution of prime factors of integers, the cycle structure of random permutations and factorization of polynomials. A probabilistic model, the "Poisson model", underlies all of these.

5:00 pm in 241 Altgeld Hall,Monday, September 17, 2018

Slow continued fractions and permutative representations of Cuntz algebras

(UIUC)

Abstract: Following the work of Bratteli and Jorgensen, I will show how permutative representations of the Cuntz algebras $\mathcal{O}_n$ arise from iterated function systems. I will then discuss a special case of this construction studied by Hayashi, Kawamura and Lascu where the function system is the Gauss map, which allows all (unitary equivalence classes of) irreducible permutative representations of $\mathcal{O}_{\infty}$ to be labeled by the orbits of a $PGL_2(\mathbb{Z})$ action. Finally, I will discuss my own work which extends this construction to $2 \leq n < \infty$ with the help of slow continued fraction algorithms.