Geometry and Topology

Speaker: Ada Boralevi (Sissa, Trieste)

"Orthogonal and unitary tensor decomposition from an algebraic perspective"

Time: 15:30

Room: MC 107

While every matrix admits a singular value decomposition, in which the terms are pairwise orthogonal in a strong sense, higher-order tensors typically do not admit such an orthogonal decomposition. In this talk I will present an intrinsic characterization of those tensors that do, by means of polynomial equations of degree at most four. The exact degrees, and the corresponding polynomials, are different in each of three times two scenarios: ordinary, symmetric, or alternating tensors; and real-orthogonal versus complex-unitary. This is a joint project with J. Draisma, E. Horobet, and E. Robeva.

Noncommutative Geometry

Speaker: (Western)

"Matrix Integrals 3"

Time: 11:00

Room: MC 108

Homotopy Theory

Speaker: Pal Zsamboki (Western)

"Higher Inductive Types (part 2)"

Time: 13:30

Room: MC 107

We start by discussing pushouts and (-1)- and 0-truncations, then we use these to discuss quotients of sets by mere relations and algebraic structures on sets. We finish with a particular case of the flattening lemma, which says that if W is a particular higher inductive type, then the total space of the fibration corresponding to a presheaf on W is equivalent to an appropriate higher inductive type.

Noncommutative Geometry

Speaker: Mitsuru Wilson (Western)

"A Gauss-Bonnet Theorem for the Noncommutative 4-sphere II"

Time: 10:30

Room: MC 108

Colloquium

Speaker: Vitali Vougalter (Toronto)

"On the existence of stationary solutions for some systems of integro-differential equations with anomalous diffusion"

Time: 15:30

Room: MC 107

The article is devoted to the proof of the existence of solutions of a system of integro-differential equations appearing in the case of anomalous diffusion when the negative Laplacian is raised to some fractional power. The argument relies on a fixed point technique. Solvability conditions for elliptic operators without Fredholm property in unbounded domains along with the Sobolev inequality for a fractional Laplace operator are being used.