Professor
Department of Mathematics
Virginia Tech University
460 McBryde
Blacksburg, VA 24061-0123
Office:   McBryde 538
Phone:   (540) 231-5053
E-Mail:  lmihalce at vt dot edu

Research Interests:

My research centers on geometry of flag varieties, with focus on Quantum (K) Schubert Calculus (i.e. the study of quantum cohomology, and quantum K theory), and the Cotangent Schubert Calculus (i.e. the study of characteristic classes of singular varieties). This is a vast area where the symmetries of flag manifolds meet the geometry of spaces of rational curves, and of the cotangent bundle. It yields a beautiful mixture of results using techniques from Algebraic Geometry (such as Intersection Theory or Schubert Calculus), Combinatorics (root systems and symmetric functions) and Geometric Representation Theory (geometry of homogeneous spaces, Hecke algebras), with bridges to areas such as Integrable Systems and further to Physics. If you wish to learn more about this and flag manifolds in general I will be happy to help. If you're using flag manifolds in your own research project, I'd be happy to hear about it.

• Research and teaching

• Publication list

• Curriculum Vitae

• During Fall 2022 Anders Buch , Rebecca Goldin , Richard Rimanyi, and I are organizing the Schubert Seminar . If you wish to register, please subscribe to the Schubert Seminar email list.

• During Fall 2022, Alex Elgart , Agnieszka Miedlar , and I are organizing the Blacksburg Math Circle. If you wish to register please go to the Math Circle website, or click on the registration form.

• Together with Jianxu Hu and Changzheng Li, I organized the International Festival in Schubert Calculus (Guangzhou, China, November 6-10, 2017). The proceedings of the conference were published by Springer.