Geometry and Topology

Speaker: Matthew Young (Chinese Univ. of Hong Kong)

"Higher Segal spaces, Hall algebras and their representations"

Time: 15:30

Room: MC 107

Higher Segal spaces, as introduced by Dyckerhoff and Kapranov, are simplicial spaces which obey combinatorial locality conditions governed by polyhedral decompositions of cyclic polytopes. Amongst other places, higher Segal spaces have found applications in homological mirror symmetry and the theory of higher categories. In this talk I will introduce a relative notion of higher Segal spaces and focus on one particular aspect of the theory- the construction of categorified Hall algebra representations.

Analysis Seminar

Speaker: Rasul Shafikov (Western)

"On dicritical singularities of Levi-flat hypersurfaces"

Time: 15:30

Room: MC 108

I will discuss a recent joint work with S. Pinchuk and A. Sukhov on characterization of dicritical singularities of Levi-flat hypersurfaces through the geometry of Segre varieties.

Speaker's web page: http://www-home.math.uwo.ca/~shafikov/

Homotopy Theory

Speaker: Marco Vergura (Western)

"Simplicial and relative categories"

Time: 13:00

Room: MC 107

We describe how simplicial and relative categories form a model of $(\infty ,1)$-categories.

Colloquium

Speaker: Kiumars Kaveh (Pittsburgh)

"Tropical geometry for matrix groups"

Time: 15:30

Room: MC 107

I will give an introduction to tropical geometry. The main philosophy is that the limit at infinity of algebraic objects (i.e. things defined by polynomials) are piecewise linear objects. Roughly speaking, the "tropical variety" of an algebraic variety is a polyhedral complex (i.e. a union of convex polyhedrons) which encodes the behavior at infinity of the variety. The fundamental theorem of tropical geometry states that different ways to define the tropical variety, using valuation map, initial ideals and (min, +) algebra are the same. Tropical geometry is intimately related to the Grobner basis theory as well as toric geometry. Finally, I will explain new developments to extend tropical geometry to subvarieties in matrix groups (e.g. GL(n)). Singular values of matrices and Smith normal forms make an appearance. For the most part the talk should be understandable for anybody with basic knowledge of algebra and geometry e.g. knowing the definition of a polynomial.