Automorphic Forms, Mock Modular Forms and String Theory (17w5097)

The Banff International Research Station will host the "Automorphic Forms, Mock Modular Forms and String Theory" workshop from October 29th to November 3rd, 2017.

It is a remarkable empirical fact, demonstrated over and over throughout history, that mathematics is the language in which the laws of Nature are written. Einstein famously asked: “How can it be that mathematics, being after all a product of human thought independent of experience, is so admirably adapted to the objects of reality?”. One possible answer is that nature strives for symmetry. There are countless of phenomena in Nature that display a remarkable amount of symmetry. For example, flowers with a very symmetrical distribution of petals have sweeter nectar and thereby attracts more bees; symmetry is thus a means for evolution to progress. Humans are also strongly attracted to symmetry, be it in architecture, mu- sic or arts. A glance at the Taj Mahal or the paintings of Escher clearly demonstrate this presence of symmetry in the world around us. Symmetry also occurs everywhere in mathematics and this is also the language in which symmetry is most naturally and accurately described. The mathematical equations that describe the building blocks of our universe display a remarkable amount of symmetry, and this was a key feature in developing them.

This workshop aims to investigate various occurrences of huge and beautiful symmetries that appear in different parts of physics and mathematics. The intriguing fact is that the same type of symmetries show up in seemingly unrelated areas and understanding why this is so is a matter of intense research which involves a very fruitful exchange of ideas and perspectives at the borderland between physics and mathematics. A apt analogy is to think of this as a kind of ’mathematical archaeology’ where scientists are uncovering closely similar structures at distant corners of the world, belonging to different epochs, and the task is to understand where these similarities come from. Ultimately this will increase our understanding of the universe we inhabit and the language in which it is written.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides
an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disc
iplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineeri
ng Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional
de Ciencia y Tecnología (CONACYT).