Department of

Mathematics

Seminar Calendar
for events the day of Friday, April 20, 2018.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 20, 2018

12:00 pm in MSTE Classroom 201, 505 E. Green Street,Friday, April 20, 2018

Three Mathematicians Walked into a Bar

Debra Woods

Abstract: 2018 marks the 25th anniversary of the MSTE Office. Debra Woods, former MSTE collaborator, will be presenting "Three Mathematicians Walked into a Bar" on Friday, April 20, from 12-1 p.m. in classroom 201, 505 E. Green St., Champaign. All are welcome, but please RSVP at https://fridaylunch.mste.illinois.edu/event/2018-04-20

12:00 pm in 443 Altgeld Hall,Friday, April 20, 2018

Dimensions results for mappings of jet spaces

Derek Jung (Illinois Math)

Abstract: In 1954, Marstrand partially answered the question: If you project a set in Euclidean space onto a plane, how does the size of the projection compare to that of the original set? I will continue work done in the past decade by Tyson with others to study this question in the sub-Riemannian setting. I will define analogues of horizontal and vertical projections in jet space Carnot groups. I will then explore how these maps affect Hausdorff dimension. About the first half of this talk will be spent defining and describing properties of these groups, which are simultaneously sub-Riemannian manifolds and Lie groups. This is recent research of the speaker.

1:00 pm in 343 Altgeld Hall,Friday, April 20, 2018

Dynamics for Smale skew products and conformal systems with overlaps

Eugen Mihăilescu (Institute of Mathematics Simion Stoilow" of the Romanian Academy)

Abstract: In this talk I will present several results in the dynamics of skew products over countable shifts of finite type, and of conformal iterated function systems with overlaps. Jointly with M. Urbanski, we proved the exact dimensionality of almost all conditional measures in fibers, and settled the problem of global exact dimensionality of equilibrium measures for Smale spaces. This is applied in particular to extending a conjecture in Diophantine approximation. Another class of skew products are obtained from iterated function systems (IFS) with overlaps. The case of arbitrary overlaps is very different from the case when the Open Set Condition is satisfied. We introduce and study asymptotic overlap numbers of measures. These numbers are then applied to dimension estimates for projections of measures on fractal limit sets, and they can be computed in certain concrete cases.

4:00 pm in 345 Altgeld Hall,Friday, April 20, 2018

Polishable Borel equivalence relations

Sławomir Solecki (Cornell)

Abstract: We introduce the notion of Polishable equivalence relations. This class of equivalence relations contains all orbit equivalence relations induced by Polish group actions and is contained in the class of idealistic equivalence relations of Kechris and Louveau. We show that each orbit equivalence relation induced by a Polish group action admits a canonical transfinite sequence of Polishable equivalence relations approximating it. The proof involves establishing a lemma, which may be of independent interest, on stabilization of increasing $\omega_1$-sequences of completely metrizable topologies.

4:00 pm in 241 Altgeld Hall,Friday, April 20, 2018

The Volume Conjecture

Xinghua Gao (UIUC)

Abstract: It is a fundamental goal of modern knot theory to “understand” the Jones polynomial. The volume conjecture, which was initially formulated by Kashaev and later generalized by Murakami^2, relates quantum invariants of knots to the hyperbolic geometry of knot complements. In this talk, I will briefly explain the volume conjecture. No background in knot theory/hyperbolic geometry/physics required.