Speaker(s)
Zhenghan Wang (Microsoft Research and UCSB)
Xiao-Gang Wen (MIT and PI)
Zheng-Yu Weng (Tsinghua)
Weiping Zhang (Nankai)
Date 2015-08-06
Venue Classroom 77201
BICMR& TIAS Math-Physics Day August 6, 2015
Organizers and Speakers:
Zhenghan Wang (Microsoft Research and UCSB)
Xiao-Gang Wen (MIT and PI)
Zheng-Yu Weng (Tsinghua)
Weiping Zhang (Nankai)
The last few decades have been a golden age for the convergence of mathematics and physics. The application of topology and global differential geometry in condensed matter physics has been a central new theme as illustrated by topological phases of matter and topological insulators. The idea of emergence and the phenomenon of entanglement hold the promise for a new quantum revolution in physics. We organize this math-physics day to encourage further activities in this integration: explaining to mathematicians by physicists what new mathematics needs to be developed, and providing further examples of the unreasonable effectiveness of mathematics in natural sciences by mathematicians.
Schedule:
August 6, Thursday
Room: Classroom 77201
Morning:
9:30am-10:30am Xiao-Gang Wen
11:00am-12:00pm Weiping Zhang
Afternoon:
2:30pm-3:30pm Zheng-Yu Weng
4:00pm-5:00pm Zhenghan Wang
Tittle and abstract:
Zhenghan Wang:
Title: TQFTs in Nature
Abstract: I will explain the search of topological quantum field theories (TQFTs) in real physical systems---topological phases of matter, and how higher category theory is useful for this endeavor.
Xiao-Gang Wen
Title: A theory of 2+1D topological orders in boson and fermion systems
Abstract: I will introduce the notion of topological order and non-Abelian statistics. Then I will use non-Abelian statistics to obtain a simplified theory that may classify 2+1D topological orders in boson and fermion systems.
Zheng-yu Weng
Title: Emergent theory of high-temperature superconductivity due to strong correlations
Abstract: Conventional condensed matter physics usually deals with weakly correlated electrons. The discovery of high-temperature cuprate superconductivitors in 1986 has inspired a tremendous effort in investigating new physics emerging from strongly correlated electrons. I will discuss a novel theoretical/mathematical structure underlying a microscopic model that may be fundamental in understanding high-Tc superconductivity, and its exotic nature may call for new mathematics.
Weiping Zhang
Title: On the mod 2 index of Atiyah and Singer
Abstract: It is said that the mod 2 index introduced by Atiyah and Singer has recently played a role in the theory of topological insulators. In this talk we will survey the mathematical aspects of this delicate invariant.
