University of Ottawa

(Carleton-uOttawa transportation information)

Place and time: UOttawa, KED B005, 11:30

- Speaker: Benoit Collins (Kyoto University, Japan)
- Title: Random graphs, random tensors, and random matrices
- Abstract: If an unoriented graph on $n$ vertices is $d$-regular, the largest eigenvalue of its adjacency matrix is $d$. Considering a nearest neighbor random walk on this graph, an important problem is the speed of convergence to the uniform measure. This is closely related to the second largest (singular) blue of the adjacency matrix. It is known that it can’t be of order substantially less than $2\sqrt{d-1}$. Graphs achieving this rate are called Ramanujan. Ramanujan graphs are in a sense optimal expander graphs. Finding such graphs is a hard problem involving number theory, with a first series of explicit examples given by Lubotzky, Phillips and Sarnak.

Graphs being $\varepsilon$-close to this $2\sqrt{d-1}$ rate are called epsilon-Ramanujan. It was proved, among others by Friedman, that for $n$ large enough, a uniformly chosen random $d$-regular graph is epsilon-Ramanujan with high probability. There exists predictions of the same flavor for the second eigenvalue of more general models of random graphs (e.g. random coverings of graphs), in particular a very general conjecture known as Alon’s generalized second eigenvalue conjecture.

In this talk, we present a solution to this long standing open problem, and generalizations. The techniques involve tools from operator algebras (liberalization tricks and norm estimates for operator valued sums of free elements) as well as the construction of a non-commutative version of non-backtracking operator theory. Time allowing, we will also describe new applications to random matrices, random tensors and operator algebras. This is based on past and ongoing collaboration with Charles Bordenave.

Place and time: UOttawa, KED B005, 2:30pm

- Speaker: Delaram Kahrobaei (University of York, UK / CUNY, USA)
- Title: Post-quantum Algebraic Cryptography
- Abstract: The National Security Agency (NSA) in August 2015 announced plans to transition to post-quantum algorithms ?Currently, Suite B cryptographic algorithms are specified by the National Institute of Standards and Technology (NIST) and are used by NSA?s Information Assurance Directorate in solutions approved for protecting classified and unclassified National Security Systems (NSS). Below, we announce preliminary plans for transitioning to quantum resistant algorithms.?

Shortly after the National Institute of Standardization and Technology (NIST) announced a call to select standards for post-quantum public-key cryptosystems.

The academic and industrial communities have suggested as the quantum-resistant primitives: Lattice-based, Multivariate, Code-based, Hash-based, Isogeny-based and group-based primitives.

In this talk I will focus on some ideas of (semi)group-based primitives. The one which was proposed to NIST is by SecureRF company based in Connecticut, among its founders there is a number theorist (Goldfeld) and two group theorists (Anshel and Anshel). They proposed a digital signature using a hard algorithmic problem in braid groups, namely conjugacy search problem.

I will then give a survey of some other suggested group-based cryptosystems that could be claimed as post-quantum cryptosystems, including my own recent work on this topic.

I will also report on a recent joint work with Faugere, Kashefi, Kaplan, Perret, Horan on "Fast Quantum Algorithm for Solving Multivariate Quadratic Equations".

Place and time: UOttawa, FTX 227, 14:30

- Speaker: Nikita Semenov (LMU Munich, Germany)
- Title: Classical motives and applications
- Abstract: Chow motives were introduced by Alexander Grothendieck in the 60s, and they have since become a fundamental tool for investigating the structure of algebraic varieties. Moreover, the motives became one of the main languages in the algebraic geometry to formulate and to solve its problems. Computing Chow motives has also proved to be valuable for addressing questions on other topics. In my talk I will explain the concept of motives and present some applications of them to classical problems in Algebra. In particular, using motives I will answer a question of Jean-Pierre Serre, under what conditions one can embed certain finite groups in the algebraic group of type E8.

Place and time: UOttawa, FTX 227, 16:00

- Speaker: Alejandro Adem (UBC, Canada)
- Title: Topology of Commuting Matrices
- Abstract: In this talk we will discuss the structure of spaces of commuting elements in
a compact Lie group. Their connected components and other basic topological properties
will be discussed. We will also explain how they can be assembled to produce a space
which classifies certain bundles and represents an interesting cohomology theory.
A number of explicit examples will be provided for orthogonal, unitary and projective
unitary groups.

Short Bio

Place and time: UOttawa, TBA

- Speaker: Gerda de Vries (University of Alberta)
- Title: TBA
- Abstract: TBA

Web-page

Place and time: HP 4351 (Macphail Room), School of Mathematics & Statistics, Carleton University, 3:30 - 4:30 (coffee & refreshments starting at 3:00)

- Speaker: J.N.K. Rao, Carleton University
- Title: On making valid statistical inferences by combining data from multiple sources
- Abstract: Abstract

Place and time: UOttawa, KED B005, 4:30-5:30

- Speaker: Baptiste Chantraine
- Title: Lagrangian submanifolds of Weinstein manifolds
- Abstract: Fukaya categories were introduced to algebraically study all Lagrangian submanifolds of a given symplectic manifolds. The rich algebraic structure underlying such categories allows sometime to reduce its study to a finite set of objects called generators of the category. Such finite generation allows to prove in some cases rigidity results on the topology of Lagrangian submanifolds. In this talk I will review the basic concepts of symplectic topology. Then I will give an overview of the construction the wrapped Fukaya category. Finally I will explain how in a joint work with Dimitroglou-Rizell, Ghiggini and Golovko we proved finite generation of the wrapped Fukaya category of Weinstein manifolds.