Dear GMS,

The speaker at today's department colloquium is Dr. Alice Lacaze-Masmonteil, our invited speaker from the University of Regina. So let's please attend if we can. See the invitation below from Dr. Karen Gunderson for more details.

After the talk at about 2:45pm, we will be holding a Q&A session about graduate study/research experience/general experience in academia with Dr. Lacaze-Masmonteil as our resource speaker. If you have some questions that you'd like us to ask for you, kindly submit them on this formhttps://forms.gle/Wrecpwti36z2f2hD6.

Also at around 5pm, we will be going for bouldering at The Hive with our guest. It will cost about $35-40 individually. Don't hesitate to join if interested, just let me know so we can arrange the transportation plans to get there. Thanks!

Best, Homer ________________________________ From: Karen Gunderson Karen.Gunderson@umanitoba.ca Sent: Tuesday, November 25, 2025 9:31 AM To: Kerry Nemet Kerry.Nemet@umanitoba.ca; Melanie Vanderhorst Melanie.Vanderhorst@umanitoba.ca Subject: Colloquium this Wednesday - Alice Lacaze-Masmonteil (Regina)

Dear colleagues,

This week's in-person Colloquium talk will be: Wednesday, 26 November at 1:30pm and held in 225 St Paul’s College.

Alice Lacaze-Masmonteil (Regina) will be speaking on “On the second largest eigenvalue of certain graphs in the perfect matching association scheme” (see abstract below). Dr. Lacaze-Mastoneil is the invited speaker of the Graduate Mathematics Society this term. Please make a special effort to attend the talks by our in-person speakers!

Next week, our in-person speaker will be Dr Yevgeniy Bilokopytov (Alberta).

As always, I am maintaining a public google calendar that you can subscribe to for up-to-date seminar information:

https://calendar.google.com/calendar/embed?src=840d5f2e955ab7313f26b18ff3b88...

Best wishes,

Karen, your colloquium coordinator

This week’s talk details:

Date and time: Wednesday November 26th, 1:30-3:00pm

Location: 225 St Paul’s College

Speaker: Alice Lacaze-Masmonteil (Regina)

Title: On the second largest eigenvalue of certain graphs in the perfect matching association scheme

Abstract: Defined as the difference between its two largest eigenvalues, the spectral gap of a graph plays an important role on our understanding of its connectivity as observed by Godsil and Royle (2001). Since computing the largest eigenvalue of a graph is generally not too difficult, the crux to understanding the spectral gap of a graph is to compute its second largest eigenvalue. In this talk, we will consider the spectral gap of certain graphs in the perfect matching association scheme. Since these graphs are part of the same association scheme, they have the same eigenspaces. These eigenspaces correspond to irreducible representations of the symmetric group and thus, one could use these irreducible representations to compute the eigenvalues of each graph. In practice, such computations are difficult to perform which makes it difficult to find the eigenspace that realizes the second largest eigenvalue. The focus of my talk will be to identify this eigenspace for selected graphs in the scheme. This is joint work with Himanshu Gupta, Allen Herman, Roghayeh (Mitra) Maleki, and Karen Meagher.