Arik Wilbert

Department of Mathematics & Statistics
University of South Alabama
Mobile, AL 36688

I am an Assistant Professor at the University of South Alabama. I obtained my Ph.D. at the University of Bonn and the Max Planck Institute for Mathematics in Bonn under the supervision of Catharina Stroppel in July 2017. Before moving to Alabama in August 2021, I was a Limited Term Assistant Professor at the University of Georgia and a Research Fellow at the University of Melbourne.

Research Interests

• Geometric & Combinatorial Representation Theory
• Categorification
• Low-Dimensional Topology & Topological Quantum Field Theory

My research is supported by an AMS-Simons PUI Grant.

Publications

Journal Articles

• Exotic Springer fibers for orbits corresponding to one-row bipartitions
  (jt. with N. Saunders), arXiv:1810.03731, Transform. Groups 27 (2022), 1111-1147
• Irreducible components of two-row Springer fibers for all classical types
  (jt. with M. S. Im and C.-J. Lai), arXiv:2011.13138, Proc. Amer. Math. Soc. 150 (2022), 2415-2432
• A study of irreducible components of Springer fibers using quiver varieties
  (jt. with M. S. Im and C.-J. Lai), arXiv:2009.08778, J. Algebra 591 (2022), 217-248
• Real Springer fibers and odd arc algebras
  (jt. with J. N. Eberhardt and G. Naisse), arXiv:2003.07297, J. Lond. Math Soc. 103 (2021), 1415-1452
• Singular TQFTs, foams and type D arc algebras
  (jt. with M. Ehrig and D. Tubbenhauer), arXiv:1611.07444, Doc. Math. 24 (2019), 1585-1655
• Two-block Springer fibers of types C and D: a diagrammatic approach to Springer theory
  (jt. with C. Stroppel), arXiv:1611.09828, Math. Z. 292 (2019), no. 3-4, 1387-1430
• Topology of two-row Springer fibers for the even orthogonal and symplectic group
  arXiv:1511.01961, Trans. Amer. Math. Soc. 370 (2018), no. 4, 2707-2737

Preprints

• Irreducible components of two-row Springer fibers and Nakajima quiver varieties*
  (jt. with M. S. Im and C.-J. Lai), arXiv:1910.03010
  *not intended for publication; superseded by arXiv:2009.08778 and arXiv:2011.13138

Books

• Geometric and Algebraic Aspects of Quantum Groups and Related Topics
  (edited with M. S. Im and B. Nguyen), AMS Contemporary Mathematics, Volume 791, 2024, 227 pages

Conference Proceedings

• Topology of two-row Springer fibers for the even orthogonal group
  Oberwolfach Reports, Volume 12, Issue 2, 2015

Theses

• Two-row Springer fibers, foams and arc algebras of type D
  Ph.D. thesis, University of Bonn, 2017
• Khovanov homology from a geometric point of view
  Master's thesis, University of Bonn, 2013
• Algebraic aspects of topological quantum field theories
  Bachelor's thesis, University of Bonn, 2011

Teaching (South Alabama)

Spring 2024

• MA 126 (Calculus 2)
  (1 section)
  
• MA 512 (Algebra 2)
  (1 section)

Fall 2023

• MA 125 (Calculus 1)
  (2 sections)
  
• MA 511 (Algebra 1)
  (1 section)

Spring 2023

• MA 227 (Calculus 3)
  (1 section)
  
• MA 536 (Real Analysis 2)
  (1 section)

Fall 2022

• MA 227 (Calculus 3)
  (1 section)
  
• MA 535 (Real Analysis 1)
  (1 section)

Spring 2022

• MA 126 (Calculus 2)
  (2 sections)
  
• MA 125 (Calculus 1)
  (1 section)

Fall 2021

• MA 125 (Calculus 1)
  (2 sections)

Teaching (UGA)

Spring 2021

• MATH 8030 (Topics in Algebra)
  (Representation Theory of Finite-Dimensional Algebras and Quivers)

Fall 2020

• MATH 2250 (Calculus 1)
  (2 sections; non-flipped)

Summer 2020

• MATH 8930 (Seminar in Algebraic Geometry)
  (Link Invariants, Categorification and Algebraic Geometry)

Spring 2020

• MATH 2250 (Calculus 1)
  (2 sections; non-flipped)

Fall 2019

• MATH 1113 (Precalculus)
  (2 sections; flipped classroom model developed by T. Alli)

Teaching (Melbourne)

Semester 1 (2019)

• Undergraduate Seminar in Algebra (Coxeter groups and Hecke algebras)
  (jt. with N. Ganter and G. Zhao)

Semester 2 (2018)

• MAST10006 (Calculus 2)
  
• MAST90097 (Algebraic Geometry)
  (jt. with A. Ram)

Semester 1 (2018)

• Graduate Seminar in Topology (Cohomology operations and the Steenrod algebra)
  (jt. with X. Gu and H. Yang)