Vitaly Lorman
Visiting Assistant Professor of Mathematics
Office  919 Hylan Building 
Email:  vlorman at ur dot rochester period edu 
CV:  curriculum vitae (10/27/2018) 
Office Hours:  Fall 2018 M 23, T 1112, W 45+by appointment 
Courses I’m teaching this semester (Fall 2018)
 MTH 161  Calculus I
 MTH 255  Differential Geometry I
Topology seminar
I coorganize the topology seminar. Talks are in Hylan 1106A, 56 on Wednesdays. There is also a pretalk, also in Hylan 1106A, 12:451:45. 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.

I am working with Apurv Nakade on lifting the (algebraic) theory of Soergel bimodules to homotopy theory. We hope this can produce something of use to representation theorists. We would also like to use this to construct a homotopy type for KhovanovRozansky’s triplygraded link homology.

Together with Nitu Kitchloo and W. Stephen Wilson I’ve made a bunch of computations with Real JohnsonWilson theories (certain cohomology theorists that come up in chromatic equivariant homotopy theory). Together with Guchuan Li and J.D. Quigley, I’m working on using them to compute some Mahowald invariants. 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 Alex Iosevich, Jonathan Passant, and a group of very bright undergraduates, we are thinking about a generalization of the Erdos distinct distance problem in combinatorial geometry. This is a continuation of an REU that Alex and I ran last summer.
Publications

Landweber flat real pairs and ER(n)cohomology, with N. Kitchloo and W.S. Wilson. Advances in Mathematics 322 (2017), 6082. arXiv link. * This paper comes with a user’s guide!.

Multiplicative structure on Real JohnsonWilson theory, with N. Kitchloo and W.S. Wilson. Contemp. Math., 707 (2018) arXiv link
 The ER(2)cohomology of BZ/(2^{q}) and CP^{n}, 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.

The Real JohnsonWilson Cohomology of CP^{∞}. Topology and its Applications 209 (2016), 367–388. arXiv link
 The ER(2)cohomology of X^{n}CP^{n} and BU(q), with N. Kitchloo and W.S. Wilson. Submitted (2018) arXiv link
REU 2018
Last summer, Alex Iosevich and I ran an REU in combinatorial geometry. It has continued into the year as an independent study.