Continuation of 1310. Applications of the integral, techniques of integration, infinite series, vectors. Credit is not given for both MATH 1220 and 1320. Prerequisite: MATH 1310 or equivalent, or instructor permission.

Seminars

Bob Oliver (U Paris 13) Local structure of finite groups and of their p-completed classifying spaces

I will discuss the close connection between the homotopy theoretic properties of the p-completed classifying space BG_p of a finite group G and the p-local group theoretic properties of G. One way in which this arises is in the following theorem originally conjectured by Martino and Priddy: for finite groups G and H, BG_p is homotopy equivalent to BH^p if and only if G and H have the same p-local structure (the same conjugacy relations among p-subgroups). Another involves a description, in terms of the p-local properties of G, of the group Out(BG_p) of homotopy classes of self equivalences of the space BG_p.

After describing the general results, I’ll give some examples and applications of both of these, especially in the case where G and H are simple Lie groups over finite fields.

Add to Google CalendarDaniel Halpern-Leistner (Columbia) - Magic windows and representations of generalized braid groups on the derived category of a GIT quotient

Abstract: One consequence of the homological mirror symmetry conjecture predicts that many varieties will have ``hidden symmetries" in the form of autoequivalences of their derived categories of coherent sheaves which do not correspond to any automorphism of the underlying variety. In fact the fundamental groupoid of a certain "complexified Kaehler moduli space" conjecturally acts on the derived category. When the space in question is the cotangent bundle of a flag variety, actions of this kind have been studied intensely in the context of geometric representation theory and Kahzdan-Lusztig theory. We establish the conjectured group action on the derived category of any variety or orbifold which arises as a symplectic or hyperkaehler reduction of a linear representation of a compact Lie group. Our methods are quite explicit and essentially combinatorial -- leading to explicit generators for the derived category of certain GIT quotients and an explicit description of the complexified Kaehler moduli space. The method generalizes the work of Donovan, Segal, Hori, Herbst, and Page which studies grade restriction rules in specific examples associated to ``magic windows."

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Michael Collins (Oxford) - Bounds for Finite Linear Groups: From Jordan and Minkowski to a Question of Serre; time 3:30-4:30

Bounds for Finite Linear Groups: From Jordan and Minkowski to a Question of Serre

Michael CollinsBounds for Finite Linear Groups: From Jordan and Minkowski to a Question of Serre

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No Math Club meeting - Fall Break

reserved for the Galois-Grothendieck seminar

*A random selection of our faculty*

MATH 1320

Continuation of 1310. Applications of the integral, techniques of integration, infinite series, vectors. Credit is not given for both MATH 1220 and 1320. Prerequisite: MATH 1310 or equivalent, or instructor permission.