- Geometry
- Topology
- Tropical Geometry
- +۲ مورد دیگر
Grigory Mikhalkin is a Full Professor at the University of Geneva, where he has been a faculty member since 2008. He is considered one of the founders of Tropical Geometry, a domain of algebraic geometry governed by (max,+)-calculus where geometric objects degenerate to their piecewise-linear limits. He leads the "ALGEBRA AND GEOMETRY" research group at the university. Mikhalkin studied at Leningrad and Michigan State University under the supervision of Oleg Viro and Selman Akbulut. After receiving his PhD in 1993, he completed postdoctoral training at Princeton, Bonn, Toronto, Berkeley, and Harvard (1993-2000). He served as associate and then full Professor at the University of Utah before moving to the University of Toronto, eventually joining the University of Geneva in 2008. Mikhalkin's primary research areas are Geometry and Topology, with a particular focus on Tropical Geometry. His work bridges algebraic geometry with combinatorial structures, exploring how complex geometric objects can be understood through their piecewise-linear tropical counterparts. This approach has proven fruitful in solving problems in enumerative geometry and has connections to mathematical physics through the study of sandpile models and self-organized criticality. His research group actively explores the connections between tropical geometry, symplectic geometry, and real algebraic geometry, organizing regular seminars including the "Séminaire Fables Géométriques." The recent publications of Professor Mikhalkin demonstrate a strong focus on the intersection of tropical geometry with sandpile models and self-organized criticality. His work has evolved to examine tropical aspects of number theory, lattice sums, and even applications to economics through auction theory. A significant portion of his recent research explores the patterns and structures that emerge in sandpile models across various lattices and dimensions, connecting discrete mathematics with continuum limits through tropical techniques. Prize of the St. Petersburg Mathematical Society (1999) Silver Medal of the Mexican Mathematical Society (2011) Canada Research Chair (2004-2009) Friedrich-Wilhelm-Bessel Research Award of the Alexander-von-Humboldt Foundation (2007-2008) European Research Council Advanced Grant (2010-2015) Chair of Fondation Sciences Mathématiques de Paris (2013-2015) Mikhalkin has successfully advised several PhD students to completion, including Kristin Shaw (2011), Lionel Lang (2014), Nikita Kalinin (2015), Mikhail Shkolnikov (2017), and Johannes Josi (2018). His research has been supported by prestigious grants including the ERC Advanced Grant and the Canada Research Chair. He presented his work at the Bourbaki seminar in 2003 and was selected as a Geometry speaker at the International Congress of Mathematicians in 2006, highlighting the significance of his contributions to the field. Professor Mikhalkin leads the "ALGEBRA AND GEOMETRY" research group at the University of Geneva, which includes current members Thomas Blomme, Francesca Carocci, Aloïs Demory, Gurvan Mével, and Antoine Toussaint. The group has a strong track record of postdoctoral fellows and alumni, including notable researchers such as Ivan Bazhov, Johan Bjorklund, Rémi Crétois, and others. They organize several seminars including the "Séminaire Fables Géométriques" and have historical connections to the Battelle Seminar and Tropical working group Seminar.
