Studies the Riemann mapping theorem, meromorphic and entire functions, topics in analytic function theory. Prerequisite: MATH 7340 or equivalent.

Seminars

Bradley Weaver (UVA) - The Local Lifting Problem and $D_4$

Abstract: The local lifting problem asks, for a fixed finite group G, whether all Galois extensions of Laurent series in characteristic p with algebraically closed residue field lift to characteristic zero. In this talk we shall discuss briefly both the connection of the local lifting problem with the motivating global lifting problem for curves and the history of the local lifting problem, and shall explain briefly why $D_4$ (the dihedral group with eight elements) satisfies the local lifting problem for p = 2.

Add to Google CalendarMartina Rovelli (EPFL) - Characteristic classes as obstructions

Abstract: Characteristic classes are invariants for principal bundles that take values in the cohomology of the base space. Every characteristic class captures different geometric features of principal bundles. In the first part of this talk, we propose a uniform treatment to interpret most of the studied characteristic classes as an obstruction to group reduction. By plugging in the correct parameters, the method recovers several classical theorems. Afterwards, we explain how the main result leads to the construction of a long exact sequence of abelian groups for any principal bundle. This sequence involves the cohomology of the base space and the group cohomology of the structure group, and the connecting map is deeply related with the characteristic classes of the bundle.

Add to Google CalendarJonathan Hall (Michigan State) - Locally defined algebras and their automorphisms

Locally defined algebras and their automorphisms

Algebras and groups often go hand-in-hand. Norton and Griess constructed certain of the sporadic finite simple groups as automorphism groups of commutative non-associative algebras. Conversely many vertex operator algebras and Jordan algebras come equipped with large groups of automorphisms. We discuss broader contexts for this. As is often the case, it is illuminated by geometry.

Jonathan HallLocally defined algebras and their automorphisms

Algebras and groups often go hand-in-hand. Norton and Griess constructed certain of the sporadic finite simple groups as automorphism groups of commutative non-associative algebras. Conversely many vertex operator algebras and Jordan algebras come equipped with large groups of automorphisms. We discuss broader contexts for this. As is often the case, it is illuminated by geometry.

" class="addtocalendar" target="_new">Add to Google CalendarHarmonic analysis and PDE seminar

UVA Math Club - Francis Bonahon (USC) - Freeways and circle packings

Some of the beauty of mathematics arises when the same principle can be used to explain very different phenomena. The talk will connect two apparently unrelated situations: finding your way through the Los Angeles freeways; and packing circles in the plane. Hint about the connection: 2-by-2 matrices. The talk will require very little mathematical background.

Add to Google CalendarIrene Pasquinelli (Durham University) - TBA

Francis Bonahon (USC) - TBA

Francis Bonahon
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MATH 7350

Studies the Riemann mapping theorem, meromorphic and entire functions, topics in analytic function theory. Prerequisite: MATH 7340 or equivalent.