#### Monday, April 24, 2017

11:00 am

Harmonic analysis and PDE seminar

317 Kerchof Hall, Charlottesville, VA, United States

Speaker:

Kelsey Goodin

Titte:

An Introduction to the Calculus of Variations

Abstract:

We can consider a special case of partial differential equations, Euler Lagrange Equations, whose solutions can be characterized as minimum values of functional equations. To solve these equations, we appeal to calculus of variations, which is a functional analytic analogue of the optimization concepts from undergrad calculus. In this talk we’ll introduce variational methods for solving PDE’s and discuss techniques for tackling non-constant boundary conditions and additional constraints. Time permitting; we’ll discuss the Weierstrass construction and fields.

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5:00 pm

UVA Math Club - Panel discussion on careers for math majors

#### Tuesday, April 25, 2017

2:00 pm

Giuseppe Martone (USC) - Positively ratioed representations and their properties.

Abstract:

For a hyperbolic metric on a surface, a classical construction of Bonahon describes the length of closed geodesics in terms of their geometric intersection number with a certain geodesic current. We generalize this picture to higher Teichm\"uller theory and to Anosov representations satisfying an additional positivity property. We use this tool to relate the entropy and the systole length of such a positively ratioed representation. This is joint work with Tengren Zhang.

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#### Wednesday, April 26, 2017

3:30 pm

Bradley Weaver (UVA) - TBA

#### Thursday, April 27, 2017

2:00 pm

Martina Rovelli (EPFL) - TBA

4:00 pm

Jonathan Hall (Michigan State) - Locally defined algebras and their automorphisms

Jonathan Hall

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 Hall
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.

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