Thursday Colloquium

Thursday, November 21st, 2024 from 3:00 pm to 3:50 pm

Host: Mason Porter

Speaker: Blair Sullivan (University of Utah)

Title: Robotic Brewing: New Inspection Planning Algorithms (IPAs) on Tap

Abstract. Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest (POIs), has applications in industrial settings, structural health monitoring, and medicine. Planning the paths for a robot to safely and efficiently perform such an inspection is an extremely difficult algorithmic challenge. In this talk, we describe a graph-based abstraction of the inspection planning problem, and how techniques from both parameterized complexity and monomial testing in algebraic circuits can be used to design new efficient algorithms when the number of desired inspection points is small. We then describe a new “reduce, partition, merge” framework that enables leveraging these algorithms to solve realistic bridge and surgical inspection instances, achieving both lower path weight and higher POI coverage than the state-of-the art approach. We conclude by discussing the current limitations of the work, along with open problems and other potential applications.

Bio: Blair D. Sullivan is a Professor in the Kahlert School of Computing at the University of Utah. Prior to joining Utah, Dr. Sullivan was an Associate Professor at NC State University, and a Research Scientist at Oak Ridge National Laboratory. She received her Ph.D. in Mathematics from Princeton University, and B.S. degrees in Applied Mathematics and Computer Science from Georgia Tech. Sullivan’s research cross-cuts the fields of data-driven science, parameterized graph algorithms, applied combinatorics, and algorithm engineering with a focus on bridging theory and practice. Her recent work has applications in computational genomics, algorithmic fairness, clustering, and robotics. In 2014, Sullivan was named one of 14 Moore Investigators in Data-Driven Discovery. She currently serves on the Steering Committee for SODA, and is Chair of the SIAM SIAG on Applied & Computational Discrete Algorithms.

Thursday, November 21st, 2024 from 4:15 pm to 5:05 pm

Host: Romyar Sharifi

Speaker: Alexander Smith (UCLA)

Title: The distribution of conjugates of an algebraic integer

Abstract. For every odd prime p, the number 2 + 2cos(2 pi/p) is an algebraic integer whose conjugates are all positive numbers; such a number is known as a totally positive algebraic integer. For large p, the average of the conjugates of this number is close to 2, which is small for a totally positive algebraic integer. The Schur-Siegel-Smyth trace problem, as posed by Borwein in 2002, is to show that no sequence of totally positive algebraic integers could best this bound.

In this talk, we will resolve this problem in an unexpected way by constructing infinitely many totally positive algebraic integers whose conjugates have an average of at most 1.899. To do this, we will apply a new method for constructing algebraic integers to an example first considered by Serre. We also will explain how our method can be used to find simple abelian varieties with extreme point counts.

Thursday, December 5th, 2024 from 3:00 pm to 3:50 pm

Host: Guido Montufar

Speaker: Christopher Hillar (Awecom, Inc.)

Title: TBD

Abstract. TBD

Thursday, December 5th, 2024 from 4:15 pm to 5:05 pm

Host: Joaquin Moraga

Speaker: Nathan Chen (Harvard)

Title: TBD

Abstract. TBD

Thursday, December 12th, 2024 from 3:00 pm to 3:50 pm

Host: Igor Pak

Speaker: Julian Sahasrabudhe

Title: The Ramsey numbers – new results and new perspectives

Abstract.In this talk I will try to motivate the interest and some of the mystery in the Ramsey numbers R(k), which are fundamental quantities in combinatorics. I will go on to discuss some recent progress on our understanding of these numbers and make some connections to problems about the geometry of random variables in high dimensions.