Geometry and Topology

Speaker: Marton Hablicsek (Univ. of Pennsylvania)

"Derived intersection over the Hochschild cochain complex"

Time: 15:30 - 16:30

Room: MC 107

In this talk I generalize a result of Behrend-Fantechi and Baranovski-Ginzburg to the 1-shifted cotangent bundle of a smooth scheme over the complex numbers. More precisely, I show how twisted cotangent bundles arise as derived intersection of Lagrangians inside the 1-shifted cotangent bundle, and how quantizations of the twisted cotangent bundles arise as derived tensor products of quantized Lagrangians.

Analysis Seminar

Speaker: Rob Corless (Western)

"The Gamma Function in the Monthly"

Time: 15:30 - 16:30

Room: MC 108

The American Mathematical Monthly has published over fifty papers on the Gamma function, factorials, or Stirling's formula.* In this talk I review (some of!) what's been said, identify some surprising lacunae, and give some easy new results. Some of this work was joint with Jonathan M. Borwein.

*One of the papers won its author, Philip J. Davis, the Chauvenet Prize in 1963. Another paper's author, Manjul Bhargava, won the 2014 Fields Medal. Other notable authors include Richard Askey, Bruce Berndt, and Walter Rudin.

Speaker's homepage: http://www.apmaths.uwo.ca/~rcorless/

Homotopy Theory

Speaker: Luis Scoccola (Western)

"Yoneda embedding for quasicategories"

Time: 13:00 - 14:30

Room: MC 107

We will discuss some basic properties of the quasicategory of spaces, presenting in particular the quasicategorical analog of theYoneda embedding.

Geometry and Topology

Speaker: Pal Zsamboki (Western)

"Semi-direct products of infinity-group sheaves"

Time: 15:30 - 16:30

Room: MC 107

We would like to get a Lie algebra functor a la SGA3 for infinity-group sheaves $G$. There, this process is based on the semi-direct product $1 \to Lie(G) \to T(G) \to G \to 1$. Therefore, we classify semi-direct products of infinity-group sheaves.

Analysis Seminar

Speaker: Edward Bierstone (Toronto)

"Global smoothing of a subanalytic set"

Time: 15:30 - 16:30

Room: MC 108

Semialgebraic and subanalytic sets have become ubiquitous in mathematics since their introduction by Lojasiewicz in the 1960s, following the famous Tarski-Seidenberg theorem on quantifier elimination. I will discuss two long-standing questions in real-analytic geometry, on global smoothing of a subanalytic set (an analogue of resolution of singularities), and on transformation of a proper real-analytic mapping to a mapping with equidimensional fibres by global blowings-up of the target (a classical result in the complex-analytic case).

These questions are related: a positive answer to the second can be used to reduce the first to the simpler semianalytic case. It turns out that the second question has a negative answer, in general, and the first nevertheless has a positive solution.

Speaker's web page: http://www.math.toronto.edu/bierston/

Homotopy Theory

Speaker: Marco Vergura (Western)

"Complete Segal Spaces"

Time: 13:00 - 14:30

Room: MC 107

We will introduce Complete Segal spaces and prove they describe an equivalent homotopy theory to the one of quasi-categories.

Colloquium

Speaker: Pierre Guillot (Strasbourg)

"Massey products and Galois cohomology"

Time: 15:30 - 15:30

Room: MC 107

Massey products are, originally, operations defined in the context of algebraic topology, on cohomology rings. However, when one specializes to group cohomology, work of Dwyer shows that the study of these operations amounts to that of elementary extension problems, involving the group of unipotent matrices over a finite field. When we specialize further, and consider Galois groups in particular, an ambitious conjecture predicts that Massey products always vanish. This has been actually proved for triple Massey products, in complete generality. In this talk, I will describe joint work with Minac, Tan, Topaz and Wittenberg, showing that the conjecture is true for fourfold Massey products in the cohomology of number fields.

Geometry and Topology

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

"Higher Segal spaces, Hall algebras and their representations"

Time: 15:30 - 16:30

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 - 16:30

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 - 14:30

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 - 16:30

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.

Analysis Seminar

Speaker: Hadi Seyedinejad (Western)

"Irreducibility in real algebraic geometry (Part I)"

Time: 15:30 - 16:30

Room: MC 108

The notion of irreducibility in the conventional Zariski topology is too coarse for real algebraic sets. For example, the hyperbola xy=1 is an irreducible algebraic set which is not even connected in the Euclidean topology. Cartan umbrella is another irreducible algebraic set, which is connected, but decomposes into the union of a 'sheet' and a 'stick.' Inspired by Nash and his notion of 'sheets,' one might require then to distinguish, as called by Kurdyka, the 'rigid pieces' of a real algebraic set. We will review different approaches to defining irreducibility and irreducible components in real algebraic geometry, in which more 'good' functions than just polynomials should be considered. We may work with the ring of Nash functions, continuous rational functions, or, most notably, arc-analytic functions. Nash functions are able to detect two components for the hyperbola xy=1. Continuous rational functions are able to detect a sheet and a stick component for Cartan umbrella. But we find examples in which only the phenomenon called 'arc-symmetricity' can among the others realize a decomposition.

Speaker's web page: http://www.math.uwo.ca/index.php/profile/59/

Noncommutative Geometry

Speaker: Bogdan Nica (McGill University)

"Hyperbolic groups and Noncommutative Geometry"

Time: 12:30 - 14:30

Room: MC 107

C*-algebras associated to groups provide some of the most interesting and most important examples in Noncommutative Geometry. In this respect, hyperbolic groups have, time and again, proved to be particularly exciting. I will discuss three vignettes illustrating this idea.