Topological Complexity Seminar - Applied Algebraic Topology Network

Applied Algebraic Topology Network via YouTube

Start learning Write review

Explore advanced topics in topological complexity through this comprehensive seminar series featuring leading researchers in applied algebraic topology. Delve into cutting-edge research presentations covering diverse aspects of topological complexity theory, including sequential parametrized topological complexity, rational approaches to complexity measures, and applications to robotics and motion planning. Examine the connections between topological complexity and various mathematical structures such as torus manifolds, Dold manifolds, sphere bundles, and configuration spaces. Learn about recent developments in discrete Morse theory, geodesic complexity of Riemannian manifolds, and the topological complexity of graph braid groups. Investigate the relationship between topological complexity and other invariants like LS-category, sectional category, and Bredon cohomology. Discover applications of these theoretical concepts to practical problems in autonomous robotics, motion planning algorithms, and enumerative geometry. Study advanced techniques including persistence methods, surgery theory applications, and the use of classifying spaces for establishing lower bounds. Gain insights into open problems and conjectures in the field, including the TC-Ganea conjecture and generalizations of classical results like Tverberg's theorem for cell complexes.

Syllabus

Jonathan Barmak: High connectivity of random simplicial complexes and their topological complexity
Soumen Sarkar (11/13/15): LS-category and topological complexity of torus manifolds & Dold manifolds
Shmuel Weinberger (10/26/25): Universal topological complexity
Facundo Memoli (10/24/25): Persistence and Topological Complexity
Nicholas Scoville (7/24/25): Discrete Morse theory: Introduction and research directions
Yuki Minowa (03/27/25): Rational sequential parametrized topological complexity
Weiyan Chen (1/23/25): Topological complexity of enumerative problems
Nursultan Kuanyshov (11/14/24): On sequential topological complexity of group homomorphisms
Ekansh Jauhari (10/24/24): On some distributional and intertwining invariants of manifolds
Shmuel Weinberger (8/29/24): Analog (and universal) complexity
Kevin Schreve (5/23/24): Right-angled Artin subgroups of graph braid groups
Arturo Espinosa Baro (3/28/24): Effective topological complexity and effective LS category
Ryuma Orita (2/22/24): Topological complexity of monotone symplectic manifolds
Amit Paul (12/14/23): Sequential parametrized topological complexity of sphere bundles
Maximilian Stegemeyer (11/9/23): Geodesic complexity and fibered decompositions of cut loci
Teresa Hoekstra (9/14/23): Bounds for the higher topological complexity of configuration spaces
Navnath Daundka (6/22/23): An upper bound on the sequential topological complexity
César Zapata (5/25/23): Higher topological complexity of a map
Rekha Santhanam (4/27/23): Higher topological complexity of Seifert fibered manifolds
Dan Guralnik (3/23/2023): Wanted: Topologists for Autonomous Robots Community
Said Hamoun (2/23/23): On the rational topological complexity of coformal elliptic spaces
Isaac Ortigoza (12/8/22): Symmetric and symmetrized topological complexity of the torus
Sam Hughes (11/10/22): Torsion homology growth and related topics
Kohei Tanaka (10/20/22): Sectional category for maps of finite spaces
Alexander Dranishnikov (9/22/22): On the LS-category of group homomorphisms
Lucile Vandembroucq (8/25/22): On the weak topological complexity and the TC-Ganea conjecture
Ben Knudsen (7/28/22): The topological complexity of pure graph braid groups is stably maximal
Clara Löh (5/28/22): Lower multiplicity bounds via classifying spaces
Stephan Mescher (3/10/22): Geodesic complexity of Riemannian manifolds
Michael Farber (2/24/22): Topological complexity of spherical bundles
Christin Bibby (12/9/21): Parametrized topological complexity of hyperplane arrangement bundles
Enrique Torres-Giese (11/11/21): Sequential Motion Planning assisted by Group Actions
Steve Scheirer (10/28/21): Relative topological complexity and configuration spaces
Jamie Scott (9/23/21): Applications of Surgery to a Generalized Rudyak Conjecture
Daisuke Kishimoto (8/12/21): Tverberg’s theorem for cell complexes
Bárbara M. Gutiérrez (7/22/21): Effectual topological complexity
José Manuel García-Calcines (6/24/21): Topological complexity using arbitrary covers
Enrique Macias-Virgo (5/27/21): Homotopic distance and Generalized motion planning
Shmuel Weinberger (4/22/21): Musing about robotic football
Matt Kahle (3/11/21): Configurations spaces of particles: homological solid, liquid, and gas
Ben Knudsen (2/11/21): Topological complexity of pure graph braid groups
Rustam Sadykov (1/28/21): On the Lusternik-Schnirelmann theory of 4-manifolds
Andrea Bianchi (12/17/20): An upper bound on the topological complexity of discriminantal varieties
Lucile Vandembroucq (11/19/20): Topological complexity for manifolds with abelian fundamental group
Mark Grant (10/22/20): Bredon cohomology and LS-categorical invariants