Visiting Assistant Professor of Mathematics
|Office||919 Hylan Building|
|E-mail:||vlorman at ur dot rochester period edu|
|CV:||curriculum vitae (10/27/2018)|
|Office Hours:||Fall 2018 M 2-3, T 11-12, W 4-5+by appointment|
Courses I’m teaching this semester (Fall 2018)
I co-organize the topology seminar. Talks are in Hylan 1106A, 5-6 on Wednesdays. There is also a pretalk, also in Hylan 1106A, 12:45-1:45. Here is our schedule–you may have to scroll down a bit.
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 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 Khovanov-Rozansky’s triply-graded link homology.
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, 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.
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!.
Multiplicative structure on Real Johnson-Wilson theory, with N. Kitchloo and W.S. Wilson. Contemp. Math., 707 (2018) arXiv link
- 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.
The Real Johnson-Wilson Cohomology of CP∞. Topology and its Applications 209 (2016), 367–388. arXiv link
- The ER(2)-cohomology of XnCPn and BU(q), with N. Kitchloo and W.S. Wilson. Submitted (2018) arXiv link
Last summer, Alex Iosevich and I ran an REU in combinatorial geometry. It has continued into the year as an independent study.