6 papers
Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the ErdÅs Problems
Tony Feng, Trieu Trinh, Garrett Bingham +21
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's ErdÅs Problems database. We emp…
Jordan decompositions in Lie algebras and their duals
Loren Spice, Cheng-Chiang Tsai
We provide a discussion of Jordan decompositions in the Lie algebra, and the dual Lie algebra, of a reductive group in as uniform a way as possible. We give a counterexample to the…
Cuspidal character sheaves on graded Lie algebras
Wille Liu, Cheng-Chiang Tsai, Kari Vilonen +1
We show in this paper that in the context of graded Lie algebras, all cuspidal character sheaves arise from a nearby-cycle construction followed by a Fourier--Sato transform in a v…
Local character expansion for mod- representations
Cheng-Chiang Tsai
Let be a -adic reductive group with ``very large.'' For any irreducible admissible representation of over an algebraically closed field of characteristic $\…
Local characters of mod- representations of a -adic reductive group
Cheng-Chiang Tsai
We define the ``lifted character'' of mod- representations of -adic reductive groups where , on compact elements with pro-orders not divisible by . We ge…
Building Machine Learning Challenges for Anomaly Detection in Science
Elizabeth G. Campolongo, Yuan-Tang Chou, Ekaterina Govorkova +148
Scientific discoveries are often made by finding a pattern or object that was not predicted by the known rules of science. Oftentimes, these anomalous events or objects that do not…