Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.

Seminars

TBA - TBA

Tea Time

Luis Pereira - On algebras over an operad

Tea Time

Igor Pak (UCLA) - Universality theorems in Algebra and Geometry

http://www.math.ucla.edu/~pak/

Universality theorems, also called the Murphy laws, are the kind of results which can be loosely described as "when things can go wrong, they so go wrong". The best known result of this type is the Mnev's Universality Theorem, characterizing realizations spaces of matroids and convex polyhedra. I will give a survey of such results from various areas including geometric combinatorics, algebraic geometry, and group theory. I will then describe what's known and our recent progress towards the Higman's Conjecture on the number of conjugacy classes of the group of upper triangular matrices over the finite

field. The talk is aimed at a general audience and hopefully will be somewhat entertaining.

Igor Pak (UCLA) - Growth of groups and Schreier graphs

http://www.math.ucla.edu/~pak/

I will give a brief survey and then discuss some recent advances on characterization of the growth of finitely generated groups, including an explicit construction of large new classes of such groups (joint with Kassabov). I will then discuss some more delicate results related to growth and expansion of Schreier graphs, and mention a number of open problems along the way.

Add to Google CalendarYajing Liu (UCLA) - L-space surgeries on links

An L-space link is a link on which all large surgeries are L-spaces. These links turn out to be rich in geometry and simple in algebra. I will present some properties and examples of L-space links in contrast to L-space knots, give bounds on the ranks of their Floer homology and on the coefficients in the multi-variable Alexander polynomials, and show that how to use Manolescu-Ozsvath link surgery formula to give a free resolution of the Floer homology of surgeries on any L-space links. As an application, we compute the whole package of Heegaard Floer homology of surgeries on 2-component L-space links only in terms of Alexander polynomial and the surgery framing.

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MATH 8880

Studies groups of transformations operating on a space; properties of fixed-point sets, orbit spaces; and local and global invariants.