Time and location
The Ottawa-Carleton joint algebra seminar meets during the academic year approximately once per week at either The University of Ottawa or Carleton University. Unless otherwise indicated, the seminar takes place on Fridays,
14:30–15:30 at the following location:
- University of Ottawa: KED B015
- Carleton University: HP 4369
For information on the seminar in past semesters, click here. To schedule a talk, please contact Hadi Salmasian.
Talks
For a complete listing of all talks at the University of Ottawa, click here.
| Date
| Speaker
| Title (click on titles to show/hide abstracts)
|
| Jan 8 (O) |
Caroline Junkins |
On the topological filtration for generalized Severi-Brauer varieties:
Abstract:
For a generalized Severi-Brauer variety X corresponding to a central simple algebra A, the Grothendieck group
of X can be described via combinatorial data related to the index and exponent of A. In this talk, we consider
how this data relates to the topological filtration of X and the Chow group of X. This is part of ongoing work
with Nicole Lemire and Daniel Krashen.
|
| Feb 26 (C) |
Elisabeth Fink (Ottawa) |
Morse geodesics in lacunary hyperbolic groups
Abstract:
A geodesic is Morse if quasi-geodesics connecting points on it stay uniformly close. If the embedding of the cyclic subgroup generated by an element is a Morse geodesic, then that element is called a Morse element. In many known examples, Morse geodesics in groups have been found via Morse elements. By studying asymptotic cones and using small cancellation, we will show how Morse geodesics can be exhibited in many lacunary hyperbolic groups, including Tarski monsters. This represents first examples of groups that have Morse geodesics but no Morse elements. I will describe further properties of non-Morse geodesics and also show how a tree can be quasi-isometrically embedded into such groups.
|
| Mar 4 (O) |
François Charette (U de M) |
Quantum Reidemeister torsion of Lagrangian submanifolds
Abstract:
Lagrangian submanifolds are important objects in the study of symplectic topology, they appear for example in integrable Hamiltonian systems. A fundamental tool to study them is Lagrangian Floer homology, however this homology often vanishes in practice. We will review the notion of torsion of an acyclic chain complex with a cyclic grading and apply it to Lagrangians with vanishing Floer homology.
|
| Mar 8 (O) |
Ugo bruzzo (SISSA) |
The Noether-Lefschetz locus of surfaces in toric 3-folds
Abstract:
A classical result states that the very general surface of degree d
larger than three in P3 has Picard number 1, and that the locus of surfaces
of degree d with Picard number greater than 1 has codimension at least d-3.
Moreover, the lower bound is reached by the families of surfaces which contain
a line. In this talk I will show how, under suitable assumptions, this can be
generalized to surfaces in (normal) projective simplicial toric 3-folds.
Joint work with Antonella Grassi.
|
| Mar 18 (O) |
Adam Logan (CSE) |
Modularity of some Calabi-Yau threefolds coming from physics
Abstract:
The correspondence between elliptic curves over $\mathbb Q$ up to isogeny and modular forms of weight $2$ (due in one direction to Eichler and Shimura, in the other mostly to Wiles) is at the heart of modern arithmetic geometry. One would like to generalize to modular forms of weight greater than $2$. Brown and Schnetz, motivated by ideas from physics, constructed certain varieties and observed that their numbers of points mod $p$ sometimes matched the coefficients of modular forms. In this talk I will explain how I proved this in two of their examples in which no variety corresponding to the modular form was previously known. Time permitting, I will also describe how I have found varieties matching other modular forms by exploring nearby regions of an appropriate moduli space (conjectural for now, but provable by a finite computation).
|
| Apr 5 (C) |
Andrei Minchenko |
Differential algebraic groups and their applications
Abstract:
At the most basic level, differential algebraic geometry
studies solution
spaces of systems of differential polynomial equations. If a matrix
group
is defined by a set of such equations, one arrives at the notion of
a
linear differential algebraic group, introduced by P. Cassidy. These
groups
naturally appear as Galois groups of linear differential equations
with
parameters. Studying linear differential algebraic groups and their
representations is important for applications to finding
dependencies among
solutions of differential and difference equations (e.g.
transcendence
properties of special functions). This study makes extensive use of
the
representation theory of Lie algebras. Remarkably, via their Lie
algebras,
differential algebraic groups are related to Lie conformal algebras,
defined by V. Kac. We will discuss these and other aspects of
differential
algebraic groups, as well as related open problems.
.
|
| Apr 8 (O) |
Daniel Barrera Salazar (CRM, Montréal) |
Overconvergent Eichler-Shimura isomorphisms for Shimura curves
Abstract:
We will discuss the p-adic variation of the Eichler-Shimura isomorphism in the context of Shimura curves. In particular, we describe the finite slope part of the space of overconvergent modular symbols in terms of the finite slope part of the space of overconvergent modular forms. As an application we will explain how to attach Galois representations to certain overconvergent modular forms. This is joint work with Shan Gao.
.
|
| May 3 (O) |
Cameron Ruether (Ottawa) |
|
(O) = uOttawa, (C) = Carleton
