# Professor Tyler Kelly PhD

School of Mathematics

Professor of Pure Mathematics

Head of Geometry and Mathematical Physics

UKRI Future Leaders Fellow

## Contact details

- t.kelly.1@bham.ac.uk

- Address
- School of Mathematics

Watson Building

University of Birmingham

Edgbaston

Birmingham

B15 2TT

UK

Professor Tyler Kelly is an algebraic geometer, specializing in its interactions in mathematical physics and mirror symmetry. Tyler is currently the head of the Geometry and Mathematical Physics group at the University of Birmingham, a group which conducts research that aims to provide new geometrical insights in problems that arise from physical theories. Tyler has broad research interests centred around mirror symmetry, a mathematical duality linking algebraic geometry and symplectic geometry originating from ideas in string theory.

Professor Kelly is a UKRI Future Leaders Fellow. Their research has been funded in the past by both a National Science Foundation Mathematical Sciences Postdoctoral Fellowship from the USA, an EPSRC Postdoctoral Fellowship, and an EPSRC New Investigator Award.

## Qualifications

- PhD in Mathematics at University of Pennsylvania, 2014
- MA in Mathematics at University of Georgia, 2009
- BS in Mathematics at University of Georgia, 2009
- AB in Romance Languages at University of Georgia, 2009

## Biography

Originally from the United States, Tyler Kelly graduated with two Bachelor's degrees and a Master's degree from the University of Georgia in 2009. Afterwards, Professor Kelly moved to Philadelphia and obtained a PhD in 2014 under the supervision of Professor Ron Donagi at the University of Pennsylvania.

At the end of the PhD, Kelly won a National Science Foundation (NSF) Postdoctoral Fellowship, which led to the University of Cambridge where Kelly spent four years, first as an NSF Fellow but then also as an EPSRC Research Fellow. While at Cambridge, Kelly was a research fellow at Homerton College.

Kelly joined Birmingham in September 2018 as part of the new Geometry and Mathematical Physics group, became a UKRI Future Leaders Fellow in 2020, and was promoted to Professor of Pure Mathematics in 2023.

Professor Kelly is a Fellow of the Higher Education Academy. At the University of Pennsylvania, they earned a graduate certificate in teaching in higher education while winning the Dean’s Award for Distinguished Teaching by a Graduate Student.

## Postgraduate supervision

Professor Kelly currently supervises two PhD students. Typically, they supervise students in algebraic geometry on problems that originate from mirror symmetry or mathematical physics.

## Research

### Research Themes

- Algebraic Geometry
- Mirror Symmetry
- Landau-Ginzburg Models
- Toric Geometry
- Zeta Functions
- Calabi-Yau varieties

### Research Activity

Professor Kelly’s research surrounds mirror symmetry. Roughly speaking, mirror symmetry allows one to encapsulate the geometry of a symplectic manifold in the algebro-geometric information of its so-called mirror algebro-geometric object. Prof. Kelly’s research primarily is focused mirror symmetry's interactions with singularity theory and noncommutative geometry. Prof. Kelly studies this in multiple ways, each having various other implications.

Kelly's main interests surround Landau-Ginzburg models, an object with origins from string theory whose applications are just now becoming fully realized mathematically. Roughly, a Landau-Ginzburg model is a triplet of data (X, G, W) where X is a quasi-affine variety, G a group acting on X and W a G-invariant complex-valued algebraic function on X. The singularity theory of the quotient of X by G and the critical locus of W are used to encode geometry. They make many problems in algebraic geometry more tractable. Professor Kelly analyses their enumerative and derived properties. Professor Kelly also has broader interest across algebraic geometry including Calabi-Yau varieties and toric varieties.

## Other activities

Co-chair for the organisation LGBTQ+ STEM

Advisory Board Member for the Academy for the Mathematical Sciences (Equality Diversity and Inclusion Workstream)

Member of the London Mathematical Society's Women and Diversity in Mathematics Committee

Local Organisation Lead for the 2020 LGBT STEMinar, held at the University of Birmingham

Staff Adviser for oSTEM (out in Science, Technology, Engineering, and Mathematics) University of Birmingham Student Chapter

## Publications

### Recent publications

#### Article

D. Favero, D. Kaplan, T. L. Kelly. Exceptional Collections of Mirrors of Invertible Polynomials. Mathematische Zeitschrift 304, 32 (2023), 16 pages.

N. Ilten, T. L. Kelly. Fano Schemes of Complete Intersections in Toric Varieties. Mathematische Zeitschrift 300 (2022) 1529-1556.

D. Favero, D. Kaplan, T. L. Kelly. A maximally-graded invertible cubic threefold that does not admit a full exceptional collection of line bundles. Forum of Mathematics, Sigma 8 (2020), Paper No. e56, 8pp.

C. Doran. T. L. Kelly, A. Salerno, S. Sperber, J. Voight, U. Whitcher. Hypergeometric decomposition of symmetric K3 quartic pencils. Research in the Mathematical Sciences 7, 7 (2020), 81 pages.

D. Favero, T. L. Kelly. Derived categories of BHK mirrors. Advances in Mathematics 352 (2019) 943–980.

C. Doran. T. L. Kelly, A. Salerno, S. Sperber, J. Voight, U. Whitcher. Zeta Functions on Alternate Mirror Calabi-Yau Families. Israel Journal of Mathematics 228 (2018), no. 2, 665-705.

D. Favero, T.L. Kelly. Fractional Calabi-Yau Categories from Landau-Ginzburg Models. Algebraic Geometry (Foundation Compositio) 5 (2018) no. 5, 596–649.

C. Doran, D. Favero, T. L. Kelly. Equivalences of Families of Stacky Toric Calabi-Yau Hypersurfaces. Proceedings of the American Mathematical Society 146 (2018), no. 11, 4633-4637.

D. Favero, T. L. Kelly. Proof of a conjecture of Batyrev and Nill. Amer. J. Math., 139 no. 6 (2017), 1493-1520.

T. L. Kelly. Picard ranks of K3 surfaces of BHK Type. Fields Institute Monographs, Calabi-Yau Varieties: Arithmetic, Geometry and Physics, 34 (2015), 45-63.

T. L. Kelly. Berglund-Hubsch-Krawitz Mirrors via Shioda Maps, Adv. Theor. Math. Phys., 17 no. 6 (2013) 1425-1449.

G. Bini, B. van Geemen, T. L. Kelly. Mirror Quintics, Discrete Symmetries, and Shioda Maps. J. Algebraic Geom., 21 (2012), 401-412.