This article was accepted into the corpus but its outbound wikilinks were never NER-processed — typical at the deepest BFS hop or when the run's entity cap was reached. No expansion funnel to show.
| Eskin, Alex | |
|---|---|
| Name | Alex Eskin |
| Birth date | 1965 |
| Birth place | Moscow |
| Nationality | Russian / United States |
| Fields | Mathematics |
| Institutions | University of Chicago, California Institute of Technology, Massachusetts Institute of Technology, University of Illinois at Chicago |
| Alma mater | Moscow State University, Princeton University |
| Doctoral advisor | Grigory Margulis |
Eskin, Alex Alex Eskin is a mathematician known for contributions to the study of dynamical systems, Teichmüller theory, and geometry of moduli spaces. He has held faculty positions at several research universities and collaborated with prominent mathematicians on problems connecting ergodic theory, algebraic geometry, and number theory. His work influenced research on translation surfaces, flat geometry, and the action of SL(2, R) on moduli spaces.
Eskin was born in Moscow and completed early studies at Moscow State University before emigrating to the United States and pursuing graduate work at Princeton University. At Princeton University he studied under Grigory Margulis and joined a community that included scholars from Institute for Advanced Study, Harvard University, and Yale University. His early influences included interactions with researchers associated with St. Petersburg mathematical traditions and contacts with émigré mathematicians in New York City and Chicago.
Eskin held positions at institutions such as Massachusetts Institute of Technology, University of Chicago, California Institute of Technology, and University of Illinois at Chicago. He was affiliated with research centers including the Institute for Advanced Study, the Simons Center for Geometry and Physics, and participated in programs at the Mathematical Sciences Research Institute and the International Centre for Theoretical Physics. He collaborated with scholars from Stanford University, Princeton University, Yale University, Columbia University, and University of California, Berkeley.
Eskin's research centers on dynamical systems on moduli spaces, particularly the action of SL(2, R) on strata of the moduli space of abelian differentials and the geometry of translation surfaces. He contributed to rigidity and classification results for invariant measures and orbit closures, working on problems related to earlier work by Marina Ratner, Howard Masur, and William Veech. Eskin, together with collaborators, proved classification theorems that built on techniques from ergodic theory, incorporating ideas from homogeneous dynamics and algebraic geometry tools related to Hodge theory and flat surfaces. Key outcomes include structure theorems for affine invariant submanifolds, finiteness results for Teichmüller curves, and applications to counting closed geodesics on translation surfaces and problems connected to Diophantine approximation and billiards in polygons. His work often interfaces with research by Curt McMullen, Maryam Mirzakhani, John Smillie, Alex Wright, and Jon Chaika.
Eskin's contributions have been recognized by prizes and invitations to major international meetings, including plenary and invited talks at the International Congress of Mathematicians, awards from organizations such as the American Mathematical Society and the National Science Foundation, and fellowships at the Institute for Advanced Study and the Simons Foundation. He has been elected to professional societies and received honors that place him among leading researchers in dynamical systems and geometry.
- Eskin, A.; Mirzakhani, M.; Mohammadi, A. "Isolation, equidistribution, and orbit closures for the SL(2,R) action on moduli space." Journal articles and preprints that appeared following presentations at venues including International Congress of Mathematicians programs and seminars at Princeton University and Stanford University. - Eskin, A.; Masur, H.; Schmoll, M. Works on counting problems for flat surfaces and billiards presented at conferences at the Mathematical Sciences Research Institute and published in leading journals. - Collaborative papers with Alex Wright and Curt McMullen on affine invariant submanifolds and related structure theorems, circulated via seminars at Harvard University and University of Chicago.
Eskin has supervised doctoral students and postdoctoral researchers who went on to positions at institutions such as Columbia University, University of Michigan, University of California, Berkeley, Northwestern University, and University of Texas at Austin. He taught graduate and undergraduate courses at Massachusetts Institute of Technology, California Institute of Technology, and University of Chicago, and his lecture series has been hosted by the Mathematical Sciences Research Institute and the Institute for Advanced Study.
Eskin has participated in outreach through public lectures at venues such as the International Congress of Mathematicians satellite events, workshops at the Simons Center for Geometry and Physics, and summer schools organized by the European Mathematical Society and the Clay Mathematics Institute. He has served on editorial boards for mathematical journals and on program committees for conferences at the American Mathematical Society and the European Mathematical Society.