The basic topology of metric spaces; continuity and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series.

Prerequisite: MATH 3310 or permission of instructor.

Published on *Department of Mathematics, U.Va.* (http://www.math.virginia.edu)

Seminars

Jean-Philippe Burelle (Maryland) - Cyclic Schottky groups and maximal representations

Fuchsian Schottky groups are explicit discrete faithful representations of free groups into PSL(2,R). Maximality of the Euler number, a topological invariant, characterizes discreteness and faithfulness. The Toledo invariant generalizes the Euler number to arbitrary Lie groups of Hermitian type. I will describe a Schottky construction for Hermitian Lie groups which corresponds exactly to maximal Toledo invariant representations.

Fuchsian Schottky groups are explicit discrete faithful representations of free groups into PSL(2,R). Maximality of the Euler number, a topological invariant, characterizes discreteness and faithfulness. The Toledo invariant generalizes the Euler number to arbitrary Lie groups of Hermitian type. I will describe a Schottky construction for Hermitian Lie groups which corresponds exactly to maximal Toledo invariant representations. " class="addtocalendar" target="_new">Add to Google CalendarSevak Mkrtchyan (U Rochester) - The point processes at turning points of large lozenge tilings

http://web.math.rochester.edu/people/faculty/smkrtchy/

In the thermodynamic limit of the lozenge tiling model the frozen boundary develops special points where the liquid region meets with two different frozen regions. These are called turning points. It was conjectured by Okounkov and Reshetikhin that in the scaling limit of the model the local point process near turning points should converge to the GUE corners process. We will discuss various results showing that the point process at a turning point is the GUE corner process and that the GUE corner process is there in some form even when at the turning point the liquid region meets two semi-frozen regions of arbitrary rational slope. The last regime arises when weights in the model are periodic in one direction with arbitrary fixed finite period.

In the thermodynamic limit of the lozenge tiling model the frozen boundary develops special points where the liquid region meets with two different frozen regions. These are called turning points. It was conjectured by Okounkov and Reshetikhin that in the scaling limit of the model the local point process near turning points should converge to the GUE corners process. We will discuss various results showing that the point process at a turning point is the GUE corner process and that the GUE corner process is there in some form even when at the turning point the liquid region meets two semi-frozen regions of arbitrary rational slope. The last regime arises when weights in the model are periodic in one direction with arbitrary fixed finite period. " class="addtocalendar" target="_new">Add to Google CalendarGreg Chadwick (Maryland) - Equivariant Segal Spaces

Abstract: The gamma G-spaces of May and Shimikawa are models for the infinite loop space of an equivariant E-infinity ring spectrum, when the group G acting is finite. Motivated by these ideas, we consider the category of simplicial G-spaces and show it admits a model structure whose fibrant objects are Segal G-spaces. These are the Segal spaces of Rezk, adapted to the equivariant setting. It follows that given a G-category, one can construct a Segal G-space in such a way that two G-categories are equivalent if and only if their corresponding Segal G-spaces are G-weak equivalent. This is joint work with Julie Bergner.

Abstract: The gamma G-spaces of May and Shimikawa are models for the infinite loop space of an equivariant E-infinity ring spectrum, when the group G acting is finite. Motivated by these ideas, we consider the category of simplicial G-spaces and show it admits a model structure whose fibrant objects are Segal G-spaces. These are the Segal spaces of Rezk, adapted to the equivariant setting. It follows that given a G-category, one can construct a Segal G-space in such a way that two G-categories are equivalent if and only if their corresponding Segal G-spaces are G-weak equivalent. This is joint work with Julie Bergner. " class="addtocalendar" target="_new">Add to Google CalendarHarmonic analysis and PDE seminar

317 Kerchof Hall, Charlottesville, VA, United States

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MATH 4310

The basic topology of metric spaces; continuity and differentiation of functions of a single variable; Riemann-Stieltjes integration; and convergence of sequences and series.

Prerequisite: MATH 3310 or permission of instructor.