## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Tuesday, August 23, 2022 1:30 PM EDT

**Catherine St-Pierre, University of Waterloo**

**"Borel fixed Ideals (in Krull dimension 0)"**

Friday, August 19, 2022 2:30 PM EDT

**Jeremy Usatine, Brown University**

**"Gromov-Witten theory and invariants of matroids"**

Wednesday, August 17, 2022 9:30 AM EDT

**Talk #1 (9:30am-10:45am): Paul Mcauley, Department of Pure Mathematics, University of Waterloo
"Vertical and Horizontal Spaces"**

For a given Riemannian manifold (M,g), a vector bundle E over M, we can define the vertical space VE which is a submanifold of TE. Given a connection on E we can then define the horizontal space HE which is a submanifold of TE. These spaces give us a fibre metric on TE and then we can look at the Levi-Civita connection in terms of these vertical and horizontal spaces.

Tuesday, August 16, 2022 1:30 PM EDT

**Sean Monahan, Department of Pure Mathematics, University of Waterloo**

**"A GIT construction for horospherical varieties"**

David Cox developed a way of writing a given toric variety as a good quotient of a quasiaffine toric variety by a diagonalizable group. This construction has a very nice interpretation using the combinatorics of the toric varieties, i.e. their fans. I will give an outline of this construction through an example, and we will see how it can be generalized to horospherical varieties.

Wednesday, August 10, 2022 9:30 AM EDT

**Talk #1 (9:30am - 10:45am): Amanda Petcu, Department of Pure Mathematics, University of Waterloo**

**“Isometric Immersion part 4”**

This talk will bring an end to our series on isometric immersions. We will define a totally geodesic immersion and a minimal submanifold. To finish we will introduce and prove the three fundamental equations: Gauss' equation, Ricci's equation, and Codazzi's equation.

**Talk #2 (11:00am - 12:15pm): Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo**

Tuesday, August 9, 2022 1:30 PM EDT

**Eric Boulter, Department of Pure Mathematics, University of Waterloo**

**"The Spectral Construction for Vector Bundles on Elliptic Surfaces"**

In general, we have a much better understanding of vector bundles on curves than on surfaces. In this talk we will look at a particular type of surface where the problem of classifying vector bundles can be partially reduced to the case of curves.

This seminar will be held jointly online and in person:

Monday, August 8, 2022 1:30 PM EDT

**Clement Wan, Department of Pure Mathematics, University of Waterloo**

**"Are pseudovarieties the finite models of a set of equations?"**

Friday, August 5, 2022 10:00 AM EDT

**Nicholas Manor, Department of Pure Mathematics, University of Waterloo**

**"Nonunital Operator Systems and Noncommutative Convexity"**

The recent work on nc (noncommutative) convex sets of Davidson-Kennedy and Kennedy-Shamovich show that there is a rich duality between the category of operator systems and the category of compact nc convex sets, leading to new insights even in the case of C*-algebras.

Thursday, August 4, 2022 10:00 AM EDT

**Nicholas Manor, Department of Pure Mathematics, University of Waterloo**

**"Quantum Channels, Exactness, and Noncommutative Convexity"**

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within our Office of Indigenous Relations.