Department of

# Mathematics

Seminar Calendar
for events the day of Thursday, April 7, 2016.

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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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Thursday, April 7, 2016

11:00 am in 241 Altgeld Hall,Thursday, April 7, 2016

#### Correlations of Farey fractions revisited

###### Florin Boca (UIUC Math)

Abstract: Existence of the correlation measures for the Farey sequence and a way of expressing them were investigated in a 2005 joint work of Zaharescu and myself. In this talk we we will discuss some potential applications to estimating the moments of eigenvalues of a certain interesting family of (non-random) large matrices. This is work in progress with Maksym Radziwill and Alexandru Zaharescu.

12:00 pm in 243 Altgeld Hall,Thursday, April 7, 2016

#### Vortex Moduli Spaces and the Space of Holomorphic Maps

###### Chih-Chung Liu (National Cheng Kung University, Taiwan)

Abstract: The space of holomorphic maps from a closed Riemann surface to complex projective space is of great physical interest. This space naturally corresponds to the space of (gauge classes of) solutions to the vortex equations on the surface. In this talk I will present my past work on strengthening the correspondence so that it is an isometry at some asymptotic region. Such a result encourages us to prove Baptista’s conjectural formula on the L^2 volume of the space of maps, generalizing Speight’s earlier result on the case for Riemann spheres.

2:00 pm in 243 Altgeld Hall,Thursday, April 7, 2016

#### Local monodromy and dimension of the branch set of generalized branched covers

###### Pekka Pankka (University of Jyväskylä, Finland)

Abstract: Discrete and open mappings are considered as generalizations of branched covers appearing in PL topology. By Väisälä's theorem such generalized branched covers are local homeomorphisms apart from a singular set of codimension at least 2. Although such generalized branched covers has been of interest from late 1960's, there are very few results on the topology of their singular and branch sets - even under additional geometric conditions. In this talk I will discuss monodromy conditions under which the singular set has exactly codimension 2 locally. This is joint work with Martina Aaltonen.

2:00 pm in Altgeld Hall 241,Thursday, April 7, 2016

#### Bilinear forms in Kloosterman sums

###### Kyle Pratt (UIUC Math)

Abstract: Many problems in analytic number theory can be reduced to finding cancellation in bilinear forms with a Kloosterman sum kernel. I'll describe some of the situations where these Kloosterman sums arise, and then, with a view towards illustrating techniques, I'll prove a general result on cancellation in bilinear forms in Kloosterman sums.