# Research

**Members of the Department of Mathematics conduct research in Mathematics and its applications. The Department's research enterprise involves all regular Faculty members, postdoctoral fellows and graduate students.**

New technologies are greatly expanding the ability to map neural systems. Reconstructions of the synaptic connections between neurons and large-scale recordings of spikes are now able to map both the structure and function of hundreds to thousands of cells. Thus, while for decades it was only possible to study the activity of only a handful of cells in a living, functional neural circuit, it is rapidly becoming possible to study activity in massive ensembles of cells during active sensory perception and sleep. With these new technologies, neuroscientists can now ask how the collective activity of hundreds or thousands of cells creates sensory and cognitive computations. The challenges posed by these increasingly large and complex datasets, however, require new and rigorous mathematical approaches in the field.

*Image by Sophie Wu*

### Faculty members of the Department of Mathematics have research interests spanning the areas of Applied Math, Analysis, Algebra, and Geometry and Topology:

Applied Math

Jason Bertram

Matt Davison

David Jeffrey

Jan Minac

Lyle Muller

Greg Reid

Lindi Wahl

Geoff Wild

Pei Yu

Xingfu Zou

Geometry and Topology

Janusz Adamus

Tatyana Barron

Dan Christensen

Graham Denham

Ajneet Dhillon

Matthias Franz

Rick Jardine

Chris Kapulkin

Masoud Khalkhali

Nicole Lemire

Jan Minac

Martin Pinsonnault

Algebra

Janusz Adamus

Taylor Brysiewicz

Dan Christensen

Graham Denham

Ajneet Dhillon

Matthias Franz

Chris Hall

Rick Jardine

Chris Kapulkin

Nicole Lemire

Jan Minac

David Riley

AnalysisJanusz Adamus

Tatyana Barron

Masoud Khalkhali

Jan Minac

Martin Pinsonnault

Rasul Shafikov

Gord Sinnamon

Some Department members specialize in areas that bridge these classifications and are applicable in other disciplines. Specific interests include stacks, derived categories, algebraic combinatorics, combinatorial algebra, number theory, graph theory, cryptography, Galois cohomology and quadratic forms, homotopy theory, higher categories, homotopy type theory, toric varieties, noncommutative geometry, quantum groups and Hopf algebras, analytic and CR-geometry, symplectic geometry, harmonic analysis, singularity theory, and mathematical physics.

See the Current Research Projects page for a description of ongoing research projects in the Department.

Please also see faculty and Postdoctoral Fellow Profiles on their respective webpages.

The Department maintains a number of active seminar and colloquia series that attract some of the world's most prominent mathematicians.

- Colloquium (recordings of our previous colloquium speakers)
- The Distinguished Lecture Series
- Algebra Seminar
- Analysis Seminar
- Geometry & Topology Seminar
- Noncommutative Geometry Seminar
- Mathematical Biology Seminar
- Dynamical Systems Seminar

For a complete list of upcoming and past events visit the Math Department Events Calendar on the home page.

### Western University is a principal sponsoring partner of the Fields Institute for Mathematical Research.

**Workshop on Noncommutative Geometry, Free Probability Theory and Random Matrix Theory**