Research Directions in Symplectic and Contact Geometry and Topology

ISBN-13: 9783030809812 / Angielski / Miękka / 2023

Opis

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field.

The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors included female and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work. 

Spis treści

A Polyfold proof of Gromov's non-squeezing theorem (K. Wehrheim).- Infinite staircases for Hirzebruch surfaces (T. Holm).- Action-angle and complex coordinates on toric manifolds (H. Lee).- An introduction to Weinstein handlebodies for complements of smoothed Toroc divisors (B. Acu).- Constructions of Lagrangian Cobordisms  (L. Traynor).- On Khovanov homology and related invariants (M. Zhang).- Braids, Fibered Knots, and Concordance Questions (D. Hubbard).

O autorze

​Bahar Acu is a Researcher in the Department of Mathematics at ETH Zürich, Switzerland. She received her Ph.D. in Mathematics from the University of Southern California, Los Angeles, USA. She was a Boas Assistant Professor of Mathematics at Northwestern University, IL, USA from 2017-2020.

 

Catherine Cannizzo is a Research Assistant Professor at the Simons Center for Geometry and Physics at Stony Brook University, USA. She holds a Ph. D. from the University of California, Berkeley, USA.

Dusa McDuff is Helen Lyttle Kimmel '42 Professor of Mathematics at Barnard College, USA.  She holds a Ph. D. from the University of Cambridge, UK.

Ziva Myer is an Assistant Research Professor at Duke University in Durham, NC, USA. She received her PhD from Bryn Mawr College in Bryn Mawr, PA, USA.

Yu Pan is an Assistant Professor at the Center of Applied Mathematics at Tianjin University, Tianjin, China. She received her Ph.D. from Duke University, USA. She was a CLE Moore Instructor at Massachusetts Institute of Technology, MA, USA from 2017-2020. 

Lisa Traynor is a Professor of Mathematics and the Class of 1897 Professor of Science at Bryn Mawr College, Bryn Mawr, PA, USA.  She obtained her Ph.D. from Stony Brook University.

Blurb

This book highlights a number of recent research advances in the field of symplectic and contact geometry and topology, and related areas in low-dimensional topology. This field has experienced significant and exciting growth in the past few decades, and this volume provides an accessible introduction into many active research problems in this area. The papers were written with a broad audience in mind so as to reach a wide range of mathematicians at various levels. Aside from teaching readers about developing research areas, this book will inspire researchers to ask further questions to continue to advance the field.

The volume contains both original results and survey articles, presenting the results of collaborative research on a wide range of topics. These projects began at the Research Collaboration Conference for Women in Symplectic and Contact Geometry and Topology (WiSCon) in July 2019 at ICERM, Brown University. Each group of authors included female and nonbinary mathematicians at different career levels in mathematics and with varying areas of expertise. This paved the way for new connections between mathematicians at all career levels, spanning multiple continents, and resulted in the new collaborations and directions that are featured in this work. 

This book is part of the Virtual Series on Symplectic Geometry.