Research Interests

I am an algebraic geometer who uses the tools around derived categories to solve problems with ties to number theory, commutative and noncommutative algebra, representation theory, theoretical physics, and symplectic geometry. My recent work studies the derived geometry of birational maps, analyzes the relationship between rationality and derived categories over general fields, and develops derived approaches to noncommutative algebraic geometry. My research has been supported by the National Science Foundation and the Simons Foundation. I have lectured on my work at over 40 institutions, on 4 continents, including Cornell, Princeton, Yale, the IAS, MSRI, the Fields Institute, BIRS, and the MFO. 

Education

• Ph.D. in Mathematics, University of Washington (2008)
• B.S. in Mathematics, California Institute of Technology (2002)

Honors and Awards

• Teaching Incubator Associate, USC College of Arts and Sciences (2019 – 2021)
• Breakthrough Star, University of South Carolina (2018)
• Invited lecture at Summer Institute in Algebraic Geometry, University of Utah (2015)
• Plenary speaker at String-Math (2014)

Experience

• Professor, University of South Carolina (2022 – present)
• Associate Professor, University of South Carolina (2018 – 2021)
• Member, Institute for Advanced Study (2016 – 2017)
• Assistant Professor, University of South Carolina (2013 – 2017)
• Senior Researcher, University of Vienna (2012 – 2013)
• Van Vleck Visiting Assistant Professor, University of Wisconsin (2011 – 2012)
• Postdoctoral Researcher, University of Pennsylvania (2008 – 2011)

Courses Taught

• MATH 141, Calculus I
• MATH 142, Calculus II
• MATH 241, Calculus III
• MATH 300, Transition to Advanced Mathematics
• MATH 544, Linear Algebra
• MATH 546, Algebraic Structures
• MATH 701, Algebra I
• MATH 702, Algebra II
• MATH 732, Algebraic Topology I
• MATH 733, Algebraic Topology II
• MATH 737, Complex Geometry I
• MATH 738, Derived Categories I
• MATH 748, Derived Categories II

Selected Publications

• Matthew Ballard, David Favero and Ludmil Katzarkov. Variation of Geometric Invariant Theory quotients and derived categories Journal für die reine und angewandte Mathematik (Crelle). Issue 746 (2019) 235--304. DOI:10.1515/crelle-2015-0096
• Matthew Ballard. Wall crossing for derived categories of moduli spaces of sheaves on rational surfaces. Algebraic Geometry 4 (3) (2017) 263--280. DOI:10.14231/AG-2017-014
• Matthew Ballard, Dragos Deliu, David Favero, M. Umut Isik, and Ludmil Katzarkov. Homological Projective Duality via variation of Geometric Invariant Theory quotients. Journal of the European Mathematical Society. Volume 19 Issue 14 (2017) 1127-1158. DOI:10.4171/JEMS/689
• Matthew Ballard, David Favero and Ludmil Katzarkov. A category of kernels for equivariant factorizations and its implications for Hodge theory, I. Publications mathématiques de l'IHÉS 120 (2014), no. 1, 1-111. DOI:10.1007/s10240-013-0059-9
• Matthew Ballard, David Favero and Ludmil Katzarkov. Orlov spectra: bounds and gaps Inventiones Mathematicae 189 (2012), no. 2, 359-430.DOI:10.1007/s00222-011-0367-y