## Current students and postdoctoral fellows

- Daniel Dallaire (MSc, NSERC Canada Graduate Scholarship, Ontario Graduate Scholarship)
- Niccolo Mattarei (PhD)
- Thomas Moran (PhD)
- Saima Samchuck-Schnarch (PhD, NSERC Canada Graduate Scholarship)

## Former students and postdoctoral fellows

### Undergraduate research students

- Patrick Cyr (Undergraduate Research Project 2022)
- Project: Frobeinus 0-Hecke algebras

- John Stuart (NSERC USRA 2020)
- Paper: Frobenius nil-Hecke algebras (with A. Savage),
*Pacific Journal of Mathematics***311**(2021), no. 2, 455–473. (arXiv) - Project: The structure of Frobenius nilHecke algebras

- Paper: Frobenius nil-Hecke algebras (with A. Savage),
- Mengwei Hu (Mitacs Globalink 2019)
- Paper: Presentations of diagram categories,
*The PUMP Journal of Undergraduate Research***3**(2019), 1–25. (arXiv)

- Paper: Presentations of diagram categories,
- Alexandra McSween (Undergraduate Research Project 2018)
- Project: Schur-Weyl duality

- Bingyan Liu (Mitacs Globalink 2018)
- Raj Gandhi (NSERC USRA 2018)
- Paper: Decomposing Frobenius Heisenberg categories,
*Journal of Algebra and Its Applications***19**, No. 05, 2050094 (2020). Winner of the Department of Mathematics & Statistics Outstanding Student Paper Prize 2018. (arXiv)

- Paper: Decomposing Frobenius Heisenberg categories,
- Alexandra McSween (Work-Study 2018)
- Project: The affine Frobenius Brauer category

- Saima Samchuck-Schnarch (NSERC USRA 2018)
- Project: An introduction to operad theory

- Dene Lepine (Undergraduate Research Project 2018)
- Paper: Monoidal supercategories and superadjunction,
*Rose-Hulman Undergraduate Journal***20**(2019), Iss. 1, Article 9.

- Paper: Monoidal supercategories and superadjunction,
- Eduardo Mendonça (Mitacs Globalink 2017)
- Project: Projective representations of groups

- Mariam Shlepchyan (NSERC USRA 2017)
- Project: The Farahat-Higman ring

- Zehui Chen (Undergraduate Research Project 2017)
- Project: Lambda-rings

- Yananan Wang (Co-op Work-Study 2017)
- Luke Volk (Work-Study 2016)
- Paper: Crystals from 5-vertex ice models (with Javier Lorca Espiro),
*Journal of Lie Theory***28**(2018), no. 4, 1119–1136. (arXiv)

- Paper: Crystals from 5-vertex ice models (with Javier Lorca Espiro),
- Ian Dewan (NSERC USRA 2016)
- Project: Graph homology and cohomology

- Edward Poon (Undergraduate Research Project 2016)
- Project: Skew group rings

- Dene Lepine (Co-op Work-Study 2016)
- Jonah Robotham (Work-Study 2016)
- Project: Highest weight categories

- Marley Liu (High school enrichment 2016)
- Project: Proof and logical argument in abstract mathematics

- Edward Poon (NSERC USRA 2016)
- Paper: Nested Frobenius extensions of graded superrings (with A. Savage),
*Involve***11**(2018), no. 3, 449–461. (arXiv)

- Paper: Nested Frobenius extensions of graded superrings (with A. Savage),
- Chad Couture (Work-Study 2015)
- Paper: Skew-zigzag algebras,
*SIGMA (Symmetry, Integrability and Geometry: Methods and Applications)***12**(2016), 062, 19 pages.

- Paper: Skew-zigzag algebras,
- Diego Berdeja Suarez (Mitacs Globalink 2015)
- Paper: Integral presentations of quantum Heisenberg algebras,
*Contemporary Mathematics***683**(2017), 247–260. (arXiv)

- Paper: Integral presentations of quantum Heisenberg algebras,
- Rabib Islam (Work-Study 2015)
- Project: Morita equivalence

- Edward Poon (Co-op Work-Study 2014)
- Paper: Category theoretic interpretation of rings,
*American Journal of Undergraduate Research***12**(2015), no. 4, 5–29.

- Paper: Category theoretic interpretation of rings,
- Matteo Copelli (Undergraduate Research Project 2014)
- Paper: Categorification of the nonnegative rational numbers,
*Rose-Hulman Undergraduate Mathematics Journal***16**(2015), no. 2, 19–37.

- Paper: Categorification of the nonnegative rational numbers,
- Wei Lu (Work-Study 2013)
- Aaron McBride (Work-Study 2013)
- Pablo Gonzalez Pagotto (Mitacs Globalink 2013)
- Jeffrey Pike (Summer Project 2012)
- Stéphane Guérin (NSERC USRA 2009)
- Andrew Sirjoosingh (NSERC USRA 2008)
- Project: An elementary proof of Gabriel's theorem

### Graduate students

- Youssef Mousaaid (PhD 2022)
- Thesis: The elliptic Hall algebra and the quantum Heisenberg category
- Paper: Affinization of monoidal categories (with A. Savage),
*Journal de l'École polytechnique – Mathématiques***8**(2021), 791-829. (arXiv) - Paper: Categorification of the elliptic Hall algebra (with A. Savage),
*Documenta Mathematica***27**(2022), 1225–1273. (arXiv) - Paper: Trivalent categories for adjoint representations of exceptional Lie algebras, submitted for publication.

- Saima Samchuck-Schnarch (MSc 2022, NSERC Canada Graduate Scholarship, Department TA of the Year 2021)
- Thesis: Frobenius Brauer categories

- Raj Gandhi (MSc 2021, NSERC Canada Graduate Scholarship, Ontario Graduate Scholarship)
- Thesis: Oriented Cohomology Rings of the Semisimple Linear Algebraic Groups of Ranks 1 and 2
- Paper: The formal affine Demazure algebra and real finite reflection groups, Algebr. Represent. Theory (2022). (arXiv)
- Paper: Diagrammatics for
*F*_{4}(with A. Savage and K. Zainoulline),*Bulletin of the London Mathematical Society*, to appear.

- Alexandra McSween (MSc 2021)
- Thesis: Affine oriented Frobenius Brauer categories and general linear Lie superalgebras
- Paper: Affine oriented Frobenius Brauer categories (with A. Savage),
*Communications in Algebra*, to appear.

- Samuel Pilon (MSc 2020, NSERC Canada Graduate Scholarship, Ontario Graduate Scholarship)
- Benjamin Dupont (PhD 2020, Université Claude Bernard Lyon 1)
- Thesis: Réécriture modulo dans les catégories diagrammatiques
- Paper: Coherent confluence modulo relations and double groupoids (with P. Malbos),
*Journal of Pure and Applied Algebra***226**(2022), no. 10, Paper No. 107037, 57 pp. (arXiv) - Paper: Rewriting modulo isotopies in pivotal (2,2)-categories,
*Journal of Algebra***601**(2022), 1–53. (arXiv) - Paper: Rewriting modulo isotopies in Khovanov-Lauda-Rouquier's categorification of quantum groups,
*Advances in Mathematics***378**(2021), 107524. (arXiv) - Paper: Confluence of algebraic rewriting systems,
*Mathematical Structures in Computer Science*, to appear. (arXiv)

- Samuel Nyobe Likeng (PhD 2020, André Dabrowski Scholarship)
- Thesis: Heisenberg categorification and wreath Deligne category
- Paper: Embedding Deligne's category Rep(
*S*) in the Heisenberg category (with A. Savage, appendix with C. Ryba),_{t}*Quantum Topology***12**(2021), no. 2, 211–242. (arXiv) - Paper: Group partition categories (with A. Savage),
*Journal of Combinatorial Algebra***5**(2021), no. 4, 269–406. (arXiv)

- Eduardo Mendonça (MSc 2020, Universidade de São Paulo, FAPESP BEFE Award)
- Thesis: Affine wreath product algebras with trace maps of generic parity
- Paper: Affine wreath product algebras with trace maps of generic parity,
*Communications in Algebra***50**(2022), no. 12, 5217–5245.

- Gang Wu (MSc 2016)
- Lucas Calixto (PhD 2015, UNICAMP, FAPESP BEFE Award)
- Thesis: Representations of map superalgebras
- Paper: Equivariant map queer Lie superalgebras (with A. Moura and A. Savage),
*Canadian Journal of Mathematics***68**(2016), 258–279. (arXiv) - Paper: Weyl modules for Lie superalgebras (with J. Lemay and A. Savage),
*Proceedings of the American Mathematical Society***147**(2019), no. 8, 3191–3207. (arXiv)

- Aaron McBride (MSc 2015)
- Joel Lemay (PhD 2015, NSERC Postgraduate Scholarship, Ontario Graduate Scholarship)
- Thesis: Geometric realizations of the basic representation of the affine general linear Lie algebra
- Paper: Geometric realizations of the basic representation of affine
*gl*,_{r}*Selecta Mathematica***22**(2016), no. 1, 341–387. Winner of the Department of Mathematics & Statistics Outstanding Student Paper Prize 2015. (arXiv) - Paper: Weyl modules for Lie superalgebras (with L. Calixto and A. Savage),
*Proceedings of the American Mathematical Society***147**(2019), no. 8, 3191–3207. (arXiv)

- Jeffrey Pike (MSc 2015)
- Thesis: Quivers and three-dimensional Lie algebras
- Paper: Quivers and three-dimensional solvable Lie algebras, Journal of Lie Theory
**27**(2017), no. 3, 707–726. (arXiv) - Paper: Twisted Frobenius extensions of graded superrings (with A. Savage), Algebras and Representation Theory
**19**(2016), no. 1, 113–133. (arXiv)

- Daniel Cicala (MSc 2014)
- Joel Lemay (MSc 2011)
- Thesis: Valued graphs and the representation theory of Lie algebras
- Paper: Valued graphs and the representation theory of Lie algebras,
*Axioms***2012**, 1(2), 111–148. (arXiv)

- Caroline El-Chaâr (MSc 2010)
- Thesis: The Onsager algebra

### Visiting students

- Javier Lorca Espiro (Universidade de São Paulo 2016)
- Paper: Crystals from 5-vertex ice models (with Luke Volk), Journal of Lie Theory
**28**(2018), no. 4, 1119–1136. (arXiv)

- Paper: Crystals from 5-vertex ice models (with Luke Volk), Journal of Lie Theory
- Tantely Rakotoarisoa (AIMS HeadStart 2014)
- Bea Schumann (University of Cologne 2012)
- Project: Representations of quivers

### Postdoctoral fellows

- Michael Reeks, 2018–2019
- Pierre-Alain Jacqmin, 2017–2019
- Tiago Macedo (CNPq Grant), 2015–2016
- Daniele Rosso, 2013–2014
- Nathan Manning, 2012–2014
- Alex Hoffnung, 2010–2012
- Prasad Senesi, 2008–2009

## Prospective students and postdoctoral fellows

### Undergraduate students

There are many opportunities for undergraduate students to gain experience in mathematical research. Applicants wishing to work with me should have a background in linear algebra (MAT 1341, 2141) and group theory (MAT 2143). Some examples of potential projects can be found here. Projects can be completed in the context of URSA awards, UROP, or Undergraduate Research Projects (see below for details). Although most projects are completed in the summer, it is also possible to do them during the fall or winter terms. Please contact me if you are interested in learning more about these possibilities.

### NSERC Undergraduate Student Research Award (USRA)

Each summer, I often have an opening for an undergraduate student as part of the NSERC USRA program. Students interested in a project to take place in the summer should contact me in December or early January. The application deadline is typically in February or March each year. See here for internal deadlines and information.

### Undergraduate Science Research Opportunity Program (USRO)

Selected students devote, during one academic year, at least 75 hours to a research project supervised by a faculty member.

### Undergraduate Research Project

Qualified undergraduate students can work on a one-semester project under the supervision of one or more faculty members in the department. At the end of the semester, the student writes a report and/or gives a seminar talk on some aspect of the research. This counts as a course (MAT4900) and is worth 3 credits.

### Graduate students

I am currently accepting graduate students. There are many intriguing problems in geometric, combinatorial, and categorical representation theory accessible at the MSc and PhD level. Students interested in working in this area should have completed courses in abstract algebra (uOttawa courses MAT3141 and MAT3143 or their equivalents). Descriptions of these uOttawa courses can be found here.

For information on available financial support and scholarships, please visit the website on funding and financing.

### Visiting student researchers

I welcome applications from undergraduate or graduate students at other institutions who would like to spend some time working under my supervision at the University of Ottawa. Such students must typically have their own funding (e.g. from their home institution) and would have the status of visiting student researcher while here at the University of Ottawa. More information on this program can be found here. For graduate students, there is also the possibility of such visits leading to co-supervision of the graduate degree. Interested students should contact me by email.

### Postdoctoral fellows

I often have an opening for a postdoctoral fellow. Applicants should be recent PhDs (or those expecting to receive their PhD before the start of the appointment) working in a field closely related to my research areas. Those interested should submit an application to the department as well as contact me personally by email.

## Research areas

Below are some examples of areas in which students under my supervision can work (as well as areas connected to the ones listed below). If you are interested in learning more about possible projects, please send me an email.

### Algebra

Abstract algebra is a very broad area of mathematics that includes linear algebra, group theory, ring theory, the theory of modules, representation theory, and much more. Most projects completed under my supervision (including those in the areas listed below) involve some field of abstract algebra. They often also involve other topics, such as geometry, topology, combinatorics, or category theory.

### Lie theory

Lie groups and Lie algebras are indispensable tools in modern mathematics and mathematical physics. Lie groups are mathematical objects that have both geometric and algebraic structure. In particular, they are simultaneously differentiable manifolds and groups. They are a mathematically precise way of studying the continuous symmetry of mathematical and physical structures. For example, in quantum physics, particles correspond to representations of Lie groups. There are many potential projects in Lie theory for undergraduate and graduate students in both classical Lie theory as well as connections between Lie theory and other subjects (see below).

### Categorification and higher representation theory

Category theory is a mathematical formalism that allows one to organize and study in an abstract way structure that is common to many different subjects. For instance, one can study properties of maps between objects and prove results that apply to maps between sets or groups. The advantage is that one does not need to reprove the results in each setting (in this case, for sets and for groups) because one has proven them in the more general setting of categories.

Recently, there has been considerable interest in using categories in a different way. This involves a process called categorification. Seeing as this field is relatively young, there are many good projects at the undergraduate and graduate level. These projects can involve connections to geometry, algebra, topology, and knot theory.

### Geometric representation theory

In general terms, geometric representation theory involves reformulating often classical results in algebra in new geometric terms. For example, one realizes a representation of a group or Lie algebra (this is a vector space on which a group or Lie algebra acts – think of a group of rotations of a plane or 3-dimensional space) as the homology of some topological space. Such realizations can yield new insight because they allow one to use geometric tools in the study of representation theory as well as representation theoretic tools in the study of geometry and topology.

## Jobs in mathematics

Are you interested in mathematics and wondering what type of career opportunities there are for mathematics majors and those with advanced degrees (MSc and PhD) in mathematics? Take a look at the following websites to learn about the many opportunities available to mathematicians.

- WeUseMath.org
- Math at Work, Canadian Mathematical Society
- Career Information, American Mathematical Society
- Mathematics Careers, Mathematical Association of America