Vesna Stojanoska

Department of Mathematics 77 Massachusetts Avenue Massachusetts Institute of Technology Cambridge, MA 02139 Office: E18-478 Email

About me

Since September 2011, I am a C.L.E. Moore Instructor at MIT. Previously, I was a graduate student at Northwestern University, working with Paul Goerss.

During the spring semester 2014 I have been participating in the Algebraic Topology program at MSRI.

My research is in stable homotopy theory, and mostly revolves around topological modular forms, duality, or both. The following are projects that I am currently involved in, listed in no particular order.

• Arithmetic duality for spectra, with Tomer Schlank.
  Tate-Poitou duality is a duality for the Galois cohomology of finite modules over the absolute Galois group of a local or global field. This arithmetic duality is reminiscent of Poincaré duality for manifolds familiar to topologists. Our goal is to upgrade this duality to apply to spectra with action by such an absolute Galois group, arriving at a Galois-equivariant Brown-Comenetz duality. This upgraded duality should lead to a better understanding of rational points on algebraic varieties.
• Cooperations in tmf-homology, with Mark Behrens, Kyle Ormsby, and Nat Stapleton.
  We combine three strategies for studying cooperations in connective topological modular forms: the Adams spectral sequence and its relation to Brown-Gitler modules following Mahowald's approach to cooperations in connective real K theory, Laures's theory of q-expansions of multi-variable modular forms, as well as level structure approximations.
• Fixed points sets of U(n)-action on the space of orthogonal decompositions of Cⁿ, with J. Bergner, R. Joachimi, K. Lesh, and K. Wickelgren.
  
• Relative Picard and Brauer groups of some ring spectra, with Akhil Mathew.
  
• Duality for topological modular forms, at the prime 2 and integrally.
  

Papers

With J. Bergner, R. Joachimi, K. Lesh, and K. Wickelgren. Classification of problematic subgroups of U(n). Preprint. Last modified: 06/30/14.

With Drew Heard, K-theory, reality, and duality. To appear in Journal of K-theory. Last modified: 06/11/14.

With J. Bergner, R. Joachimi, K. Lesh, and K. Wickelgren. Fixed points of p-toral groups acting on partition complexes. To appear in Proceedings of the Women in Topology BIRS workshop. Last modified: 04/20/14.

With Mark Behrens, Kyle Ormsby, and Nat Stapleton. On the ring of cooperations for 2-primary connective topological modular forms. A very preliminary draft. Last modified: 01/20/14 .

Calculating descent for 2-primary topological modular forms. To appear in Contemporary Mathematics volume Proceedings of the Fourth Arolla Conference in Algebraic Topology. Last modified: 09/05/13.

Duality for topological modular forms. Documenta Math. 17 (2012), 271--311. Last modified: 09/05/13.

With Orlin Stoytchev, Touching the Z/2 in three-dimensional rotations , Math.Mag. 81 (2008), no. 5, 345-357.

Presentations and more

Part I, Part II, Part III , Part IV of a lecture series at the Young Women in Topology Meeting 2012

Slides for a talk at the Special Session on Homotopy Theory at the 2012 AMS Joint Meetings

Some spectral sequences drawn using Tilman Bauer's sseq package.

Teaching

Fall 2013

Recitation leader for 18.02 Multivariable calculus

Spring 2013

18.024 Calculus with theory (Part 2)

Fall 2012

18.014 Calculus with theory (Part 1)

Fall 2011 and Spring 2012

Recitation leader for 18.02 Multivariable calculus