Chris Brav

Bio

Christopher Brav will join the Shanghai Institute for Mathematics and Interdisciplinary Sciences (SIMIS) as Professor from August 2024. Currently he is a Lead Scientific Researcher at the Centre of Pure Mathematics at the Moscow Institute of Physics and Technology. He obtained his Ph.D. in Mathematics at Queen’s University in 2008, after which he was a post-doc at the University of Toronto, Leibniz University Hannover, and Oxford University. Before moving to the Faculty of Mathematics at the Higher School of Economics in Moscow, he spent a year as a member of the Institute for Advanced Study in Princeton.

Professor Brav is working on the relation between Calabi-Yau categories (non-commutative analogues of Calabi-Yau manifolds) and shifted symplectic geometry of moduli spaces, as well as on using condensed mathematics to study infinite dimensional shifted symplectic spaces appearing in representation theory and mathematical physics. His work has been published in leading journals including Compositio Mathematica, Geometry and Topology, Journal of the American Mathematical Society, and Selecta Mathematica.

Education Experience

• 2008 Queen’s University, Kingston, Ontario Doctor
• 2003 Queen’s University, Kingston, Ontario Master
• 2002 St. Olaf College, Northfield, USA Bachelor

Work Experience

• 2022- Moscow Institute of Physics and Technology, Centre for Pure Mathematics, Dolgoprudny, Russia Lead Researcher
• 2020-2022 Higher School of Economics, Faculty of Mathematics, Moscow, Russia Associate Professor
• 2014-2020 Higher School of Economics, Faculty of Mathematics, Moscow, Russia Assistant Professor
• 2013-2014 Institute for Advanced Study, School of Mathematics, Princeton, USA Member
• 2011-2012 Oxford University, Mathematical Institute, Oxford, UK Post-doctoral fellow
• 2010-2011 Leibniz University, Graduiertenkolleg 1463: Analysis, Geometry and String Theory, Hannover, Germany Post-doctoral fellow
• 2008-2010 University of Toronto, Department of Mathematics, Toronto, Canada Post-doctoral fellow

Honors and Awards

Publications

1. Non-commutative calculus, connections, and loop spaces. Updated December 10, 2023 With N. Rozenblyum. In preparation.
2. Hamiltonian flows in Calabi-Yau categories. With N. Rozenblyum. In preparation.
3. Beilinson-Parshin adeles via solid algebraic geometry. With G. Konovalov. In preparation.
4. The cyclic Deligne conjecture and Calabi-Yau structures. With N. Rozenblyum. arXiv:2305.10323
5. Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli space of objects. With T. Dyckerhoff. Selecta Mathematica 27, 63 (2021).
6. Relative Calabi-Yau structures. With T. Dyckerhoff. Compositio Mathematica 155, no. 2 (2019): 372-412.
7. A Darboux theorem for derived schemes with shifted symplectic structure. With V. Bussi, and D. Joyce. Journal of the American Mathematical Society 32, no. 2 (2019): 399-443.
8. A Darboux theorem for shifted symplectic structures on derived Artin stacks. With O. Ben-Bassat, V. Bussi, and D. Joyce. Geometry & Topology 19, no. 3 (2015): 1287-1359.
9. Symmetries and stabilization for sheaves of vanishing cycles. With V. Bussi, D. Dupont, D. Joyce, and B. Szendr˝oi. Journal of Singularities 11 (2015): 85-151.
10. Thin monodromy in Sp(4). With H. Thomas. Compositio Mathematica 150, no. 3 (2014): 333-343.
11. Braid groups and Kleinian singularities. With H. Thomas. Mathematische Annalen 351, no. 4 (2011): 1005-1017.
12. The projective McKay correspondence. International Mathematics Research Notices 2009, no. 8 (2009): 1355-1387.