Studies the basic structure theory of associative or nonassociative algebras.

Seminars

David Brydges (UBC)

Title:

The Lace expansion for the $|\varphi|^4$ model

Abstract:

Akira Sakai has shown that a convergent lace expansion exists for the Ising and $\varphi^4$ models. He uses the current representation for the Ising model to convert the system to a percolation. In work with Tyler Helmuth and Mark Holmes we give a different expansion based on the Symanzik local time isomorphism. This expansion exists for $|\varphi|^4$, O(n) models and the continuous time lattice Edwards model (n=0), but we can only prove convergence for n=0,1,2 because the GHS inequalities are not known to hold for n>2. As in all other lace expansions, for convergence a small parameter is required. Thus the method gives information on critical exponents for the listed models in high dimensions, or for

finite but sufficiently long range coupling.

Luis Pereira (UVA) -A (equivariant) tree description of (genuine equivariant) operads

Abstract: A well known phenomenon in equivariant homotopy theory is that objects with $G$-actions naturally give rise to more complex objects: for example, if X is a $G$-space, then $\pi_n(X)$ forms a coefficient system of abelian groups or, similarly, if $\mathcal{C}$ is a $G$-equivariant topological category then its homotopy category $ho(\mathcal{C}$ is a coefficient system of categories.

However, the situation is more subtle if $\mathcal{O}$ is a $G$-equivariant topological (perhaps colored) operad, in which case the (similarly constructed) homotopy operad $ho(\mathcal{O})$ is not simply a coefficient system of operads, but rather a more complex object that we call a “genuine equivariant operad”.

The combinatorics of genuine equivariant operads are encoded by $G$-trees (which are related, but not quite, trees with an action of $G$), and in this talk I will explain how the former can be built by exploring a few key constructions on the latter. Specializing to the case $G=*$ the trivial group, we obtain a description of (regular) operads that appears to be somewhat novel.

This is joint work with Peter Bonventre.

Alan Reid (U Texas Austin) - Geometry, topology and arithmetic of canonical curves

Geometry, topology and arithmetic of canonical curves

Let K be a knot in S^3 with hyperbolic complement. The seminal work of Thurston, and Culler-Shalen established the SL(2,C)-character variety X(K) as a powerful tool in the study of the topology of M. The canonical component C is a component of X(K) that contains the character of a faithful discrete representation. Thurston proved that the canonical

component is a curve. In this talk we will discuss some recent work in the direction of trying to understand what “these curves look like” as well as properties of these curves, their relation to the topology of S^3\K and arithmetic properties of Dehn surgeries on K.

Geometry, topology and arithmetic of canonical curves

Let K be a knot in S^3 with hyperbolic complement. The seminal work of Thurston, and Culler-Shalen established the SL(2,C)-character variety X(K) as a powerful tool in the study of the topology of M. The canonical component C is a component of X(K) that contains the character of a faithful discrete representation. Thurston proved that the canonical

component is a curve. In this talk we will discuss some recent work in the direction of trying to understand what “these curves look like” as well as properties of these curves, their relation to the topology of S^3\K and arithmetic properties of Dehn surgeries on K.

Harmonic analysis and PDE seminar

317 Kerchof Hall, Charlottesville, VA, United States

Speaker:

Peter Perry (U Kentucky)

Titte:

TBA

Abstract:

TBA

Add to Google CalendarJean-Philippe Burelle (Maryland) - TBA

*A random selection of our faculty*

MATH 8855

Studies the basic structure theory of associative or nonassociative algebras.