Patrick Brosnan

Patrick Brosnan (* 1968 in Philadelphia ) is an American mathematician.

Brosnan grew up in Corpus Christi , Texas, received his bachelor's degree in mathematics from Princeton University in 1991 and received his PhD from the University of Chicago with Spencer Bloch in 1998 ( Topics in Algebraic Geometry: An Algebraic Napier-Ramachandran Theorem and Steenrod Operations on Chow Groups ). He was at Northwestern University , the Max Planck Institute for Mathematics in Bonn, the University of California, Irvine , the University of California, Los Angeles , the State University of New York at Buffalo and the Institute for Advanced Study in Princeton. before becoming a professor at the University of British Columbia . He is a professor at the University of Maryland .

Brosnan studies algebraic geometry, motifs, algebraic cycles, Hodge theory, algebraic groups, algebraic combinatorics, analytic number theory, and mathematical physics.

He is best known for rebutting the Spanning Tree Conjecture by Maxim Kontsevich (1997) in 2003 with Prakash Belkale . It concerns the number-theoretical properties of Feynman graphs of a simple model theory of quantum field theory, the theory. It was part of a theory of the mathematical properties of Feynman graphs developed by David Broadhurst and Dirk Kreimer from the perturbative treatment of quantum field theories. Kontsevich hypothesized that the function which gives the number of points on the hypersurface belonging to the Feynman graph over finite fields (with , p prim) is a polynomial in q. The conjecture was numerically well confirmed (and it applies to lower order Feynman graphs) and the rebuttal came as a surprise at the time. ${\displaystyle \phi ^{4}}$ ${\displaystyle \mathbb {F} _{q}}$ ${\displaystyle q=p^{n}}$

He expanded the concept of the essential dimension of Zinovy ​​Reichstein and Joe Buhler in algebra within the framework of the theory of algebraic stacks and applied this, for example, with Reichstein and Angelo Vistoli to square shapes. They proved that the essential dimension of the spinor group of quadratic forms with trivial discriminants and Hasse-Witt invariants grows exponentially and that the theory of these forms was richer than previously assumed.

With Gregory J. Pearlstein he proved the finiteness of the number of zeros of non-trivial admissible normal functions on curves. These play a role in a program that has as a long-term objective evidence of the Hodge Conjecture (one of the Millennium Problems ).

In 2009 he received the Coxeter James Prize .

Web links

• Homepage
• CMS, recognition of the Coxeter James Prize

Individual evidence

1. ↑ Patrick Brosnan in the Mathematics Genealogy Project (English)
2. ↑ Belkale, Brosnan Matroids motives, and a conjecture of Kontsevich , Duke Math. J., Volume 116, 2003, pp. 1-188.
3. ↑ Brosnan, Reichstein, Vistoli Essential dimension, spinor groups and quadratic forms , Annals of Mathematics, vol 171, 2010, 533-544.
4. ^ Brosnan, Pearlstein The zero locus of an admissible normal function , Annals of Mathematics, Volume 170, 2009, pp. 883-897.