vlorman

Vitaly Lorman

Vitaly Lorman

Visiting Assistant Professor of Mathematics


Office 919 Hylan Building
E-mail: vlorman at ur dot rochester period edu
CV: curriculum vitae (10/15/2019)
Spring 2019 Office Hours: M 5-6, W 2-3:30, and by appointment

Courses I’m teaching this semester (Spring 2019)

Topology seminar

I co-organize the topology seminar. Talks are usually in Hylan 1106A, 4-5 on Wednesdays. Here is our schedule–you may have to scroll down a bit.

Research

I study algebraic topology. I am particularly interested in computations related to equivariant and chromatic homotopy theory, as well as applications to geometric problems (such as the immersion problem for projective spaces and computing cobordism rings). I’ve also recently developed an interest in link invariants related to various link homology theories. Scroll down the page for my publications and preprints.

What I’m currently working on:
  • I am working with Carl McTague and Doug Ravenel on computing the String cobordism ring at the prime 3. It is, in Doug’s words, a computational circus. Here are some pictures of the Adams spectral sequence computing the homotopy groups of MString at p=3.

  • I am working with Apurv Nakade on lifting Khovanov and Rozansky’s triply graded link homology (which categorifies the HOMFLY-PT polynomial) to homotopy theory.

  • Together with Nitu Kitchloo and W. Stephen Wilson I’ve made a bunch of computations with Real Johnson-Wilson theories (certain cohomology theorists that come up in chromatic equivariant homotopy theory). Together with Guchuan Li and J.D. Quigley, we proved some theorems generalizing classical blueshift results in chromatic homotopy theory to the equivariant setting. Some other things I’ve been thinking about: extending HKR character theory to these Real cohomology theories, using our blueshift results to compute some Mahowald invariants, various questions regarding ER(n)-orientability of vector bundles. I’m also interested in finding a way to use unstable ER(n)-operations (which one can say a lot about) to say something about the immersion problem for projective spaces.

  • Together with Semin Yoo, I am working with a group of very bright undergraduates on some problems related to generalizing knot tricolorability. This is a continuation of a mini-course in the STEM For All program that we ran last summer.

Publications

  1. Tate blueshift and vanishing for Real oriented cohomology, with G. Li and J.D. Quigley. Soon to be submitted (2019). arXiv link

  2. Landweber flat real pairs and ER(n)-cohomology, with N. Kitchloo and W.S. Wilson. Advances in Mathematics 322 (2017), 60-82. arXiv link. * This paper comes with a user’s guide!.

  3. Multiplicative structure on Real Johnson-Wilson theory, with N. Kitchloo and W.S. Wilson. Contemp. Math., 707 (2018) arXiv link

  4. The ER(2)-cohomology of BZ/(2q) and CPn, with N. Kitchloo and W.S. Wilson. Canad. J. Math. 70 (2018), no. 1, 191?217. arXiv link.
    • Here are some pictures of the AHSS for CP, computed in the paper, that Steve Wilson made.
  5. The Real Johnson-Wilson Cohomology of CP. Topology and its Applications 209 (2016), 367–388. arXiv link

  6. The ER(2)-cohomology of XnCPn and BU(q), with N. Kitchloo and W.S. Wilson. Topology and its Applications (2019), to appear. arXiv link

STEM For All 2019

Last summer, Alex Iosevich and I organized the Stem For All summer program at U of R. With the help of Semin Yoo I taught a mini-course on Knot Theory for two weeks which was followed by a research program in which we worked on generalizing p-colorability of knots. We are continuing to work on this project in the academic year.

REU 2018

In the summer of 2018, Alex Iosevich and I ran an REU in combinatorial geometry. It continued into the year as an independent study.