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 Events
UBC Math
Fri 28 Sep 2018, 4:00pm
Department Colloquium
ESB 2012
Integers in many-body quantum physics
ESB 2012
Fri 28 Sep 2018, 4:00pm-5:00pm

Abstract

Although integers are ubiquitous in quantum physics, they have different mathematical origins. In this colloquium, I will give a glimpse of how integers arise as either topological invariants or as analytic indices, as is the case in the so-called quantum Hall effect. I will explain the difficulties arising in extending well-known arguments when one relaxes the approximation that the particles effectively do not interact with each other in matter. Recent advances have made such realistic generalizations possible.

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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UBC Math
Fri 5 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
Cluster theory of the coherent Satake category
ESB 2012
Fri 5 Oct 2018, 4:00pm-5:00pm

Abstract

The affine Grassmannian, though a somewhat esoteric looking object at first sight, is a fundamental algebro-geometric construction lying at the heart of a series of ideas connecting number theory (and the Langlands program) to geometric representation theory, low dimensional topology and mathematical physics.

Historically it is popular to study the category of constructible perverse sheaves on the affine Grassmannian. This leads to the *constructible* Satake category and the celebrated (geometric) Satake equivalence.

More recently it has become apparent that it makes sense to also study the category of perverse *coherent* sheaves (the coherent Satake category). Motivated by certain ideas in mathematical physics this category is conjecturally governed by a cluster algebra structure.

We will illustrate the geometry of the affine Grassmannian in an elementary way, discuss what we mean by a cluster algebra structure and then describe a solution to this conjecture in the case of general linear groups.

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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UBC Math
Fri 12 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
PIMS/ UBC Math Faculty Award colloquium: TBA
ESB 2012
Fri 12 Oct 2018, 4:00pm-5:00pm

Abstract

TBA

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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University of Toronto
Fri 19 Oct 2018, 4:00pm
Department Colloquium
ESB 2012
CRM-Fields-PIMS prize lecture: TBA
ESB 2012
Fri 19 Oct 2018, 4:00pm-5:00pm

Abstract

TBA

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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University of Southern California
Fri 9 Nov 2018, 4:00pm
Department Colloquium
ESB 2012
Rising Stars Colloquium - Thinking inside the box: a combinatorial approach to Schubert calculus
ESB 2012
Fri 9 Nov 2018, 4:00pm-5:00pm

Abstract

Schubert calculus began in the 1880s when Hermann Schubert began asking enumerative questions in geometry, such as how many lines in space are incident to four given lines. Efforts to build a rigorous foundation for these questions led to the development of cohomology rings and modern intersection theory. In the 1980s, Lascoux and Schutzenberger defined an explicit basis for polynomials, called Schubert polynomials, whose structure constants precisely compute these intersection numbers. For the special case of the grassmannian sub variety of the complete flag manifold, these polynomials are Schur polynomials and the classical Littlewood—Richardson rule gives their structure constants by enumerating Yamanouchi tableaux, which are certain ways of putting numbers into boxes. In this talk, I’ll survey combinatorial models for Schubert polynomials that generalize these tableaux models for Schur polynomials and lead to new cases for computing structure constants by enumerating new ways of putting numbers in boxes.
 

Note for Attendees

Refreshments will be served in ESB 4133 from 3:45 p.m.-4:00 p.m.
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