Dr Tyler Kelly PhD

Dr Tyler Kelly

School of Mathematics
Lecturer

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr. Kelly is an algebraic geometer, specializing in its interactions in mathematical physics and mirror symmetry. As a member of the Geometry and Mathematical Physics group at the University of Birmingham, Dr. Kelly and colleagues conduct research that provides new geometrical insights in problems that arise from physical questions and discoveries. Dr. Kelly’s publications include results in algebra, number theory, and geometry.

Dr. Kelly has broad research interests centred around mirror symmetry, a duality originating from string theory that has now provided a mathematical link between algebraic geometry and symplectic geometry. Dr. Kelly with collaborators has used this intuition to study aspects of number theory as well. This research is currently funded by an Engineering and Physical Science Research Council (EPSRC) New Investigator Award, and has been funded by both a National Science Foundation Mathematical Sciences Postdoctoral Fellowship from the USA and an EPSRC Fellowship.

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, Dr. Kelly moved to Philadelphia and obtained a PhD in 2014 under the supervision of Prof. Ron Donagi. In addition, Dr. Kelly gained a graduate certificate in teaching in higher education while winning the Dean’s Award for Distinguished Teaching by a Graduate Student.

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

Dr. Kelly joined Birmingham in September 2018 as a lecturer in mathematics as part of the new geometry and mathematical physics group. He has now won an EPSRC New Investigator Award (September 2019 - August 2021).

Teaching

During the 2019-20 academic year, Dr. Kelly is teaching the Spring 2020 portion of Metric Spaces and Topology.

Postgraduate supervision

Dr. Kelly currently has one PhD student and is interested in supervising students in algebraic geometry or number theory on problems that originate from mirror symmetry or mathematical physics. Dr. Kelly also has interests in supervising projects on Landau-Ginzburg models, toric varieties, and combinatorial aspects of mirror symmetry.

Research

Research Themes

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

Research Description

Dr. Kelly’s research surrounds mirror symmetry. Mirror symmetry is a duality in geometry that links algebraic geometry and symplectic geometry. Dr. Kelly’s research primarily is focussed on the question of finding a corresponding space W to a symplectic object M so that the symplectic geometry of M is encoded in the algebraic geometry W.  Dr. Kelly studies this in multiple ways, each having various other implications.

Dr. Kelly is interested in derived categories both in the context of mirror symmetry but also for understanding algebraic varieties themselves. Previous work includes using derived categories to link various complete intersections in toric varieties. Dr. Kelly researches Landau-Ginzburg models, an object with origins from string theory whose applications are just now becoming fully realized mathematically. Despite the complicated name, Landau-Ginzburg models are quite concrete as a structure, though their usage is a bit contextual. Dr. Kelly analyzes their enumerative and derived properties. Dr. Kelly also studies in the geometry and arithmetic of Calabi-Yau varieties as well as toric varieties.

Other activities

Member of the London Mathematical Society

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

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

Publications

  • 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.