Canadian Mathematical Society, Ottawa, ON K1G3V4
613-733-2662 ext 733
meetings@cms.math.ca

# Students

2019 CMS Summer Meeting, Regina, SK, June 7-10

With the support of CRM, the Fields Institute, and PIMS grants are available to partially fund the travel and accommodation costs for bona fide graduate students at a Canadian or other university and CMS student members.  Click here to become a CMS Student Member.

Preference is given to Canadian students. To apply for this funding, applicants should ask their supervisor or departmental graduate advisor to complete the online application form no later than April 30.

Applicants will be notified late in April of the funding decision. If successful, the student will receive a cheque for reimbursement of expenses after the meeting and upon completion and submission of the standard Travel Expense Claim Form, along with appropriate original receipts.

### Student Poster Session

Organizers: Asmita Sodhi (Dalhousie) and Yuliya Nesterova (Queen’s)

studc-summer19-poster@cms.math.ca

Students are encouraged to present a poster with a topic of their choice on Saturday, June 8th. To register for the poster session, the abstract has to be submitted and registration has to be paid by May 17.

Setup will take place on Friday, June 7th starting at 3:00 pm, or on Saturday, June 8th before 8:30 am. Presenters are asked to give a short (~3min) presentation to the judges and remain at their posters during judging to answer questions. The winners will be announced following the judging time period. Prizes are awarded at the banquet on Sunday, June 9th to the three best poster presenters, based on content, organization, and presentation. Each winner will receive two complimentary tickets to the banquet as well as $100 and a framed award certificate. ###### OrganizersYuliya Nesterova (Queen's University)Daniel Zackon (University of Toronto) ### Student Research Presentations ###### Sunday June 9 University of Regina The Canadian Mathematical Society Student Committee (CMS Studc) invites students (undergraduate and graduate) to present a talk on a topic of their choice at the Student Research Presentations Session during the 2019 CMS Summer Meeting. These presentations should introduce the student’s research to a general mathematical audience. Any questions about the student sessions should be directed to the student session organizers at: To register for the session, contact the organizers of the session with a draft abstract by May 15. Notice of acceptance will be given by May 17. Abstracts submitted after this deadline will be considered if space remains. Presenters will also have to register for the meeting. Student members of the CMS who are presenting a poster or talk have significantly reduced registration costs ($30 until May 6, $45 thereafter). If you are not currently a member of the CMS, talk to your department chair about the possibility of becoming a university-sponsored student member for a reduced fee. ###### Student Presenters Asmita Sodhi (Dalhousie University) Integer-valued polynomials and a game called$p$-ordering In this talk we will visit the world of integer-valued polynomials, and also introduce the ring of polynomials that are integer-valued over a subset of$\mathbb{Z}$. We will explore Bhargava’s “game called$p$-ordering”, and see how$p$-orderings and$p$-sequences allow us to find a$\mathbb{Z}$-module basis for the ring of integer-valued polynomials for a subset of the integers. Finally, we will briefly see how Bhargava’s tools may be extended to the noncommutative case of integer-valued polynomials over the ring$M_n(\mathbb{Z})$of$n\times n$integer matrices. Nicole Kitt (University of Calgary) How to calculate perverse sheaves on quiver representation varieties of type A In their 1997 paper, Geometric construction of crystal bases, Masaki Kashiwara and Yoshihisa Kashiwa Saito described a singularity in a quiver representation variety of type$A_5$with the property that the characteristic cycles of the singularity is reducible, thus providing a counterexample to a conjecture of Kazhdan and Lusztig. This singularity is now commonly known as the Kashiwara-Saito singularity. While the 1997 paper showed that the characteristic cycles of the Kashiwara-Saito singularity decomposes into at least two irreducible cycles, they promised, but did not prove, that it decomposes into exactly two irreducible cycles.\\ The goal of this project is to complete this calculation using geometric techniques developed in the example part of the Voganish paper. The first step in this calculation is to compute perverse sheaves on the quiver representation variety of type$A_5$. In this talk, I will illustrate the methods used to make such a calculation by calculating perverse sheaves for a specific quiver representation variety of type$A$. In doing so, I will show how to construct a proper smooth cover for any quiver variety of type$A$. Anne Dranowski (Univeristy of Toronto) MV cycles from generalized orbital varieties Representations constructed from the geometry of homogeneous spaces involve many choices, so we would like to parametrize coarse invariants, like dimensions of weight spaces of irreducible representations, by combinatorial objects. A classical example is the Grothendieck–Springer resolution of the variety of nilpotent elements$\mathcal{N}\$ in a semi-simple Lie algebra: the top Borel-Moore homology of a fibre of this resolution is an irreducible representation of the associated Weyl group. In type A, a canonical basis is parametrized by Young tableaux. This talk will review a more modern example: the torus-equivariant cohomology of upper-triangular Slodowy slices. We explain the representation theory and combinatorics of this example: using the geometric Satake correspondence and a Spaltenstein decomposition, we show that orbital varieties in Slodowy slices define bases in representations. Under the magnifying glass of a finer geometric invariant — the Duistermaat-Heckmann measure — we show that not all bases are created equal.

Reila Zheng (Univeristy of Toronto)

Random walks on Gromov hyperbolic spaces

I will describe the geometry of Gromov hyperbolic spaces, Gromov boundary, Poisson boundary, shadow sets, horofunctions, and other useful constructs. I will also introduce some tools from probability theory used to analyze random walks of isometries on such spaces. If time allows I will state some recent results in literature and sketch their proofs.