Programs

During the 2021–2022 academic year, the CMSA will host a program on the so-called “Swampland.” The Swampland program aims to determine which low-energy effective field theories are consistent with nonperturbative quantum gravity considerations. Not everything is possible in String Theory, and finding out what is and what is not strongly constrains the low energy...

Recent developments have poised this area to make serious advances in 2019, and we feel that bringing together many of the relevant experts for an intensive semester of discussions and collaboration will trigger some great things to happen. To this end, the organizers will host a small workshop during fall...

During Academic year 2018-19, the CMSA will be hosting a Program on Mathematical Biology. Just over a century ago, the biologist, mathematician and philologist D’Arcy Thompson wrote “On growth and form”. The book was a visionary synthesis of the geometric biology of form at the time. It also served as a call...

During Academic year 2018-19, the CMSA will be hosting a Program on Topological Aspects of Condensed Matter. New ideas rooted in topology have recently had a big impact on condensed matter physics, and have highlighted new connections with high energy physics, mathematics and quantum information theory. Additionally, these ideas have found applications...

arge random matrices provide some of the simplest models for large, strongly correlated quantum systems. The statistics of the energy levels of ensembles of such systems are expected to exhibit universality, in the sense that they depend only on the symmetry class of the system. Recent advances have enabled a...

Most physical phenomena, from the gravitating universe to fluid dynamics, are modeled on nonlinear differential equations. The subject also makes close connections with other branches of mathematics. In particular, some of the deepest results in complex geometry and topology were obtained through solutions of nonlinear equations. The subject underwent rapid...

In the past thirty years there have been deep interactions between mathematics and theoretical physics which have tremendously enhanced both subjects. The focal points of these interactions include string theory, general relativity, and quantum many-body theory. String theory has been at the center of the ongoing effort to uncover the...

A major challenge in evolutionary biology is to understand how spatial population structure affects the evolution of social behaviors such as cooperation. This question can be investigated mathematically by studying evolutionary processes on graphs. Individuals occupy vertices and interact with neighbors according to a matrix game. Births and deaths occur...

The methods of topology have been applied to condensed matter physics in the study of topological phases of matter. Topological states of matter are new quantum states that can be characterized by their topological properties. For example, the first topological states of matter discovered were the integer quantum Hall states....

The Simons Collaboration on Homological Mirror Symmetry brings together a group of leading mathematicians working towards the goal of proving Homological Mirror Symmetry (HMS) in full generality, and fully exploring its applications. This program is funded by the Simons Foundation. Mirror symmetry, which emerged in the late 1980s as an unexpected physical duality between quantum field...

The Simons Collaboration program in Homological Mirror Symmetry at Harvard CMSA and Brandeis University is part of the bigger Simons collaboration program on Homological mirror symmetry (https://schms.math.berkeley.edu) which brings to CMSA experts on algebraic geometry, Symplectic geometry, Arithmetic geometry, Quantum topology and mathematical aspects of high energy physics, specially string theory...