25/02/2022

IMPA will have a Thematic Program in vertex and chiral algebras.

How can we give a rigorous mathematical meaning to quantum field theories? Originating in the 20th century, this is one of the main challenges in theoretical physics. Vertex algebras and chiral algebras are mathematical objects of representation theory that emerged as an attempt to solve this problem, and have increasingly aroused the curiosity of researchers. Therefore, IMPA is promoting a Thematic Program during the first semester of this year, with a series of activities on vertex algebras and chiral algebras.

The “ Thematic Program on Vertex and Chiral Algebras ” will be held in a hybrid format, with part of the program taking place at IMPA headquarters and broadcast via videoconference. Registration is available at this link . The Thematic Program will launch on March 1Wednesdays with a school featuring five mini-courses led by leading scholars in the field. The following week, from March 21st to 2Thursdays, there will be an international workshop bringing together approximately 20 speakers. The complete program is available on the event website .

“We hope that the Program can stimulate and strengthen the interaction between people in theoretical physics and pure mathematics. Our expectation is that graduate students can take advantage of the lectures and courses as an introduction to the area of representation theory,” says Jethro Van Ekeren, a member of the event committee and professor at the Federal Fluminense University (UFF), who will join the IMPA research staff in March. IMPA researcher Reimundo Heluani also organizes the Program.

Van Ekeren gives special emphasis to the lectures that will address a new connection between theoretical physics and vertex algebras called 4D/2D dualities. "It's a novelty that has recently emerged in the field and is attracting a lot of interest from both sides." For the researcher, one of the most interesting aspects of the topic covered in the Program is its interface with different areas of knowledge, such as topology and theoretical physics. "Works that have explored these relationships, such as that of Richard Borcherds, have been recognized with the Fields Medal."