Geometry and Topology

The geometry and topology group at UB is traditionally strong in research and mentoring. Our faculty work in the areas of algebraic topology, complex geometry, differential geometry, geometric group theory, and geometric topology.

Image: Relativity by M.C. Escher. Licensed under Fair use via Wikipedia.

Image: Relativity by M.C. Escher, 1953. Licensed under Public Domain via Wikimedia Commons.

Faculty

Also on this page:

FACULTY RESEARCH AREAS

Complex and Differential Geometry
Cowen, Michael
Faran, James
Ramachandran, Mohan

Contact Geometry and Topology
Kutluhan, Cagatay
Menasco, William

Geometric Group Theory
Mangahas, Johanna

Homotopy Theory
Badzioch, Bernard

Low-Dimensional Topology
Kutluhan, Cagatay
Mangahas, Johanna
Menasco, William
Sikora, Adam
Zhang, Xingru

Quantum Topology
Sikora, Adam

Symplectic Geometry
Kutluhan, Cagatay

WEEKLY SEMINARS

Due to existence of multiple online seminars, the UB geometry and topology seminar will not run until at least Spring 2021. The 2019-20 seminar listing plus further updates can be found, here

CURRENT PhD STUDENTS AND FACULTY ADVISORS

  • Linda Alegria (Menasco)
  • Charles Cain (Badzioch)
  • Hong Chang (Menasco)
  • Yen-Lin Chen (Kutluhan)
  • Carolyn Engelhardt (Kutluhan)
  • Yuan Liu (Ramachandran)
  • Yuqing Ma (Badzioch)
  • Michael Montoro (Sikora)
  • Deepisha Solanki (Menasco)
  • Bratati Som (Mangahas)
  • Yuxun Sun (Badzioch)
  • Daxun Wang (Mangahas)
  • Bojun Zhao (Zhang)

RECENT PhD GRADUATES (and faculty advisors)

2021
Subhankar Dey, PhD (Kutluhan) "On Heegaard Floer Theoretic Properties of Knots"

Hakan Doga, PhD (Kutluhan) "A Combinatorial Description of the Concordance Invariant Epsilon"

Xifeng Jin, PhD (Menasco) "Geodesics in the Curve Graph and Heegaard Distance"

Marc Schilder, PhD (Zhang) "The A-Polynomial and Knot Volume"

 

2020
Wei Lin, PhD (Menasco) "On Crossing Ball Structure in Knot and Link Complements"

Chen Zhou, PhD (Ramachandran) "Lefschetz Theorem for Holomorphic One-forms on Weakly 1-complete Manifolds"


2019
Alyson Bittner, PhD (Badzioch) "Detecting Mapping Spaces and Spaces with Complexity One"

Abdalrazzaq Zalloum, PhD (Mangahas) "Beyond Hyperbolicity; Generalizing Classical Results from Hyperbolic groups to all Finitely Generated Groups"


2018
Robert Tuzun, PhD (Sikora) "Computational Search for Nontrivial Knots with Unit Jones Polynomial"


2017
Xiao Wang, PhD (Ramachandran) "Complex Hyperbolic Manifolds and Structures of Exotic Hyperbolic Manifolds"

Mark Nieland, PhD (Menasco) "Connected-Sum Decompositions of Surfaces with Minimally-Intersecting Filling Pairs"


2016
Dennis Ruppe, PhD (Zhang) "On the AJ-conjecture for certain families of satellite knots"

Matthew Sartwell, PhD (Badzioch) "Detecting Mapping Spaces and Derived Equivalence of Algebraic Theories"


2015
Watchareepan Atiponrat, PhD (Menasco) "Obstructions to Decomposable Exact Lagrangian Fillings"
 

2014
Blake Winter (Sikora) "Virtual, Welded and Ribbon Links in Arbitrary Dimensions"
 

2013
Bruce Corrigan-Salter, PhD (Badzioch) "Rigidification of Homotopy Algebras over Finite Product Sketches"
 

2011
Gregory Schneider, PhD (Menasco) "On the Classication of Legendrian Rational Tangles via Characteristic Foliations of Compressing Discs" 
 

2010
Xiao Guo, PhD (Zhang) "Two classes of Virtually Fibered Montesinos Links of Type SL_2"

Douglas LaFountain, PhD (Menasco) "On The Uniform Thickness Property And Contact Geometric Knot Theory"

Yu Zhang, PhD (Zhang) "Lifted Heegaard surfaces and virtually Haken manifolds"