Mathematical Papers and Preprints

1. Genus-zero r-spin theory, (with Renzo Cavalieri and Rob Silversmith), 28 pages, to appear in Moduli (Foundation Compositio).

2. Open FJRW theory and mirror symmetry (with Mark Gross and Ran Tessler), 140 pages.

3. Mirror symmetry for open r-spin invariants, (with Mark Gross and Ran Tessler), Pure and Applied Mathematics Quarterly 20, no 2 (2024) 1005-1024.

4. Exceptional Collections for Mirrors of Invertible Polynomials, (with David Favero and Daniel Kaplan), Mathematische Zeitschrift 304,  32 (2023) 16 pages.

5. Fano Schemes of Complete Intersections in Toric Varieties, (with Nathan Ilten), Mathematische Zeitschrift 300 (2022), 1529-1556. 

6. A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles, (with David Favero and Daniel Kaplan), Forum of Math, Sigma, volume 8, edition 56 (2020), 1-8.

7. Hypergeometric decomposition of symmetric K3 quartic pencils, (with Charles F. Doran, Adriana Salerno, Steven Sperber, John Voight, and Ursula Whitcher), Research in the Mathematical Sciences 7, 7 (2020), 81 pages.

8. Derived Categories of BHK Mirrors, (with David Favero), Advances in Mathematics 352 (2019), 943-980.

9. Alternate mirror families and hypergeometric motives, (with Charles F. Doran, Adriana Salerno, Steven Sperber, John Voight, and Ursula Whitcher), 2017 MATRIX Annals, eds. David R. Wood, Jan de Gier, Cheryl E. Praeger, and Terence Tao, MATRIX Book Series 2 (2019),  441-448.

10. Zeta functions of alternate mirror Calabi-Yau families, (with Charles F. Doran, Adriana Salerno, Steven Sperber, John Voight, and Ursula Whitcher), Israel Journal of Mathematics 228 no. 2 (2018), 665-705.

11. Fractional Calabi-Yau Categories from Landau-Ginzburg Models, (with David Favero), Algebraic Geometry 5 no. 5 (2018), 596-649.

12. Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces, (with Charles F. Doran and David Favero), Proceedings of the American Mathematical Society 146 (2018), 4633-4647.

13. Proof of a Conjecture of Batyrev and Nill, (with David Favero), American Journal of Mathematics 139 no. 6 (2017), 1493-1520.

14. Picard Ranks of K3 Surfaces of BHK Type, Fields Institute Monographs, Calabi-Yau Varieties: Arithmetic, Geometry and Physics 34 (2015), 45-63.

15. Berglund-Hubsch-Krawitz Mirrors via Shioda Maps, Advances in Theoretical and Mathematical Physics, 17 no. 6 (2013), 1425-1449.

16. Mirror Quintics, discrete symmetries and Shioda Maps (with Gilberto Bini and Bert van Geemen) Journal of Algebraic Geometry, 21 (2012), 401-412.

17. On Kostant's Theorem for Lie Algebra Cohomology (with UGA VIGRE Algebra Group), Contemporary Mathematics, 478 (2008), 39-60.

Other Publications:

Best practice for LGBTQ+ data collection by professional organizations (with A. Bond), Nature 626, 261 (2024).

• • Supplementary resource: A quick guide to data collection for LGBTQ+ characteristics (with A. Bond), figshare.

Research Support

My research over my career has been supported through the following national grants:

• 2024-2027: UKRI Future Leaders Fellowship, Renewal MR/Y033841/1

• 2024-2025: EPSRC Small Grant EP/Y033574/1 (joint with Dan Kaplan)

• 2020-2024: UKRI Future Leaders Fellowship MR/T01783X/1

• 2019-2022: EPSRC New Investigator Award EP/S03062X/1

• 2015-2019: EPSRC Research Fellowship - Postdoctoral EP/N004922/1

• 2014-2018: NSF Mathematical Science Postdoctoral Research Fellowship DMS-1401446

• 2009-2014: NSF Graduate Research Fellowship

Seminars

We host a weekly Geometry and Mathematical Physics Seminar at Birmingham during the term. Please check here for the current schedule.

There are also a couple regional geometry seminars that are fairly local to Birmingham: COW and EMSG.

Research Supervision:

I have supervised the following Postdocs:

• Qaasim Shafi (Sept 2022-present)

• Shengyuan Huang (Sept 2021-present)

• Dan Kaplan (Jan 2020-Dec 2021)

I have supervised the following PhD students:

• Thais Gomes Ribeiro (2023-present)

• Rob Maher (2020-present)

• Aimeric Malter (2019-2023)

Future events:

Mirrors in the Midlands 2024 - August 6-9, 2024

Shengyuan Huang, Qaasim Shafi and I are co-organising the next installment of mirror symmetry workshops at Birmingham, Mirrors in the Midlands, this Summer.

Spec(\overline{\mathbb{Q}[2πi]}) - June 24-27, 2024.

Renzo Cavalieri, Melody Chan, Jared Weinstein and I are co-organising the extension of Spec(\overline{\mathbb Q}). This conference is designed to celebrate and promote research advances of LGBT2Q mathematicians in algebraic geometry, arithmetic geometry, commutative algebra and number theory at the Fields Institute.

Past events:

COW meets EAGLE - February 2-3 2023

Michel van Garrel, Anne-Sophie Kaloghiros, Timothy Logvinenko, Alan Thompson and I are co-orgnised a conference on enumerative algebraic geometry at the University of Birmingham. This is in part to celebrate the lectureship of Michel van Garrel at Birmingham.

Spec(\overline{\mathbb Q}) - July 6-8, 2022 

Juliette Bruce, Renzo Cavalieri, John Voight and I are co-organised a conference to celebrate and promote research advances of LGBT2Q mathematicians in algebraic geometry, arithmetic geometry, commutative algebra and number theory at the Fields Institute.

Geometry of Gauged Linear Sigma Models - June 21-24, 2022

Ed Segal, Shengyuan Huang and I are co-organised a conference on the Geometry of Gauged Linear Sigma Models at the University of Birmingham.

LGBT STEMinar 2020 - 10 January 2020

I was the local organisational lead for the  LGBT STEMinar 2020, which we hosted at the University of Birmingham. It was the biggest yet, with 250 attendees! Check out LGBTQ+ STEMinar website for further events. 

Undergraduate Summer School on Homological Algebra of Mirror Symmetry - July 29 - August 2, 2019.

Ursula Whitcher and I organised the undergraduate summer school for the Fields Institute's Thematic Program on the Homological Algebra of Mirror Symmetry. 

Mirrors in the Midlands - April 1-3, 2019

Andrea Brini and I organised this conference at Birmingham.