Curriculum vitae

download cv (pdf)

Postdoctoral Research Positions

2020 - present: King's College London
Feb - Aug 2021: Imperial College London
2018 - 2020: University of Birmingham
2017 - 2018: Instituto de Matemáticas de la UNAM Unidad Oaxaca

Grants

Researcher co-I on EPSRC grant (£460,000)
LMS Scheme 5 (£2, 721)

Graduate Education

2012 - 2017: University of Texas at Austin, Ph.D. in Mathematics
Advisor: Sean Keel
2010 - 2012: University of Texas at Austin, Physics
Transferred to Mathematics

Students

Edward Quilty

(MSci co-supervisor, graduated 2020)

Research Interests

Mirror symmetry
Cluster varieties
Toric varieties
Convex geometry
Combinatorial representation theory

I study mirror symmetry for cluster varieties and generalizations of toric geometry to the cluster world. This involves a generalization of convex geometry to piecewise-linear (tropical) spaces and its algebro-geometric interpretations. There are many applications in combinatorial representation theory.

Teaching

Lectures

Spring 2023: Toric Varieties
Designed and taught grad course on toric varieties. View notes
Fall 2021: Introduction to Algebra
Covered 2 weeks of lectures & exercise sessions during professor’s paternity leave

Tutorials

Spring 2022: Linear Algebra and Geometry II
Fall 2021: Groups and Symmetries
Fall 2016: Differential Equations with Linear Algebra
Spring 2016: Algebraic Structures II
Fall 2015: Algebraic Structures I
Fall 2013: Differential Calculus for Scientists
Spring 2013: Differential Calculus
2010 - 2013: Introduction to Modern Physics

Directed Reading Program mentor

Spring & Fall 2014 Spring 2016: Guiding an undergraduate math student though an independent study.
Topics included cluster varieties, mathematical physics, and representation theory.

Seminars and Conferences Organized

Conferences

upcoming (June 2024): Mirror Symmetry for Cluster Varieties and Representation Theory
(co-organizer)

Seminars

Fall 2023 - Spring 2024: King’s College London Geometry Seminar
(co-organizer)
Fall 2020: Symplectic Cut Seminar
(co-organizer)
Fall 2019 - Spring 2020: Birmingham Geometry and Mathematical Physics Seminar

Articles

Compactifications of cluster varieties and convexity: Joint with M.-W. Cheung, and A. Nájera Chávez
Published in International Mathematics Research Notices (2021); read in journal

read on arXiv
Newton–Okounkov bodies and minimal models for cluster varieties: Joint with L. Bossinger, M.-W. Cheung, and A. Nájera Chávez; read on arXiv
Toric degenerations of cluster varieties and cluster duality: Joint with L. Bossinger, J. B. Frías-Medina, and A. Nájera Chávez
Published in Compositio Mathematica (2020); read in journal

read on arXiv
Quantization of deformed cluster Poisson varieties: Joint with M.-W. Cheung, and J. B. Frías-Medina
Published in Algebras and Representation Theory (2023); read in journal

read on arXiv
Littlewood-Richardson coefficients via mirror symmetry for cluster varieties: read in journal

read on arXiv
Fock-Goncharov conjecture and polyhedral cones for $U \subset \mathrm{SL}_n$ and base affine space $\mathrm{SL}_n/U$: read on arXiv

Selected Research Talks

5 May 2023: Fanosearch seminar
Imperial College London, UK
22 Mar 2023: Algebra and Number Theory seminar
University of Glasgow, UK
8 Dec 2022: Toric Degenerations worksop
Banff International Research Station, Canada
Nov 2022: Mini-course: From toric varieties to cluster varieties
Centro de Ciencias Matem ́aticas UNAM Campus Morelia, Mexico
25 May 2022: Bridges between representation theory and algebraic geometry conference
University of Leeds, UK
13 Apr 2021: Bath Algebra, Geometry and Number Theory seminar
University of Bath, UK
19 Feb 2021: Geometry & Topology seminar
Imperial College London, UK
4 Dec 2020: Conferencias en Geometría Algebraica
Centro de Ciencias Matem ́aticas, UNAM Campus Morelia, Mexico
10 Mar 2020: University of Edinburgh Algebra seminar
University of Edinburgh, UK
27 Feb 2020: MFO Mini-Workshop: Superpotentials in Algebra and Geometry
Oberwolfach, Germany
21 Jan 2020: University of Warwick Algebraic Geometry seminar
University of Warwick, UK
9 Oct 2019: King’s College London Geometry seminar
King’s College London, UK
16 Jul 2019: 5CinG workshop: Mirror symmetry and cluster algebras
University of Cambridge, UK
10 Jul 2019: SIAM Conference on Applied Algebraic Geometry: Cluster Algebras and Positivity
Universit ̈at Bern, Switzerland
28 May 2019: Cambridge Algebraic Geometry Seminar
University of Cambridge, UK
1 Nov 2018: Rutgers Geometry, symmetry, and physics seminar
Rutgers University, New Brunswick, New Jersey, USA
23 Oct 2018: Harvard Algebraic geometry seminar
Harvard University, Cambridge, Massachusetts, USA
21 Oct 2018: AMS Special Session: Cluster algebras, Poisson geometry, and related topics
University of Michigan, Ann Arbor, Michigan, USA
8-9 May 2018: Lecture series at CINVESTAV (5h)
CINVESTAV, Mexico City, Mexico
23 Mar 2018: Frobenius structures and relations workshop
University of Glasgow, UK
15 Mar 2018: Tropical Geometry meets Representation Theory workshop
Universität zu Köln, Cologne, Germany
30 Jan 2018: Cluster varieties and mathematical physics workshop
Casa Matemática Oaxaca, Mexico
30 Nov 2017: US-Mexico Conference of Representation Theory, Categorification, and Non-commutative Algebra
Instituto de Matemáticas de la UNAM, Mexico City