Contact:gyan@nd.edu

Research Interests:

• I'm thinking about stuff related to the slice spectral sequence of BP_R^{((C_{2^n}))} with XiaoLin Danny Shi and Yutao Liu. 

• I'm thinking about some equivariant F_2-synthetic spectra with Mark Behrens.

• I'm thinking about maximal compatibility of transfer systems with David DeMark, Mike Hill, Yigal Kamel, Nelson Niu, Kurt Stoekl and  Danika van Niel.

• I'm thinking about global and equivariant formal group laws with Noah Wisdom and Jack Carlisle.

Publications and Preprints:

1. Generalized Tate diagrams of equivariant slice spectral sequences, with XiaoLin Danny Shi and Yutao Liu. In preparation.

2. Real Global Group Laws and Hu-Kriz Maps, with Jack Carlisle and Noah Wisdom. (arxiv, 2025).

3. On the structure of the RO(C_{p^n})-graded homotopy of Eilenberg-MacLane spectra, with Igor Sikora. Accepted by A&GT. (arxiv, 2023)

4. The RO(C_{2^n})-graded homotopy of HF_2. Accepted by Proceedings of the AMS. (arxiv, 2023)

5. The RO(C_{2^n})-graded homotopy of HZ through generalized Tate squares. Accepted by La Matematica. (arxiv, 2022) 

6. The Green functor structure of RO(D_{2p})-graded cohomology of a point. Submitted. (arxiv, 2023)

Work in progress:

1. Equivariant F_2-synthetic spectra, with Mark Behrens. In preparation.

2. Disk-like transfer systems and their maximal pairs, with David DeMark, Mike Hill, Yigal Kamel, Nelson Niu, Kurt Stoekl, and Danika van Niel. In preparation.

Notes:

1. On the Klein four equivariant homotopy of HF_2(partial result). (Klein Four, 2022)

2. The RO(C_4)-graded homotopy of HA. (C_4 HA, 2023 )

3. A localization theorem for equivariant spectra. (Localization Theorem, 2023)

Invited Talks:

1. The generalized Tate diagrams of equivariant slice filtration. AMS Sectional Meeting at the University of Kansas. March 2025.

2. The generalized Tate diagrams of equivariant slice filtration. JMM 2025 homotopy theory session. Jan 2025.

3. The generalized Tate diagrams of equivariant slice filtration. UIUC topology seminar. Dec 2024.

4. The generalized Tate diagrams of equivariant slice filtration. University of Kentucky topology seminar. Nov 2024.

5. Equivariant computations using generalized Tate diagrams. New Mexico State University topology seminar. Oct 2024.

6. The generalized Tate diagrams of equivariant slice spectral sequences. UCLA algebraic topology seminar. April 2024.

7. The generalized Tate diagrams of equivariant slice spectral sequences. UCSD topology seminar. Feb 2024.

8. The generalized Tate diagrams of equivariant slice spectral sequences. University of Washington topology seminar. Feb 2024.

9. The generalized Tate diagrams of equivariant slice spectral sequences. UChicago algebraic topology seminar. November 2023.

10. RO(C_{2^n})-graded homotopy of HZ and HF_2. AMS Fall Central Sectional Meeting. October 2023.

11. RO(C_{2^n})-graded homotopy of Eilenberg Maclane spectra. UCSD topology seminar. June 2023.

Contributed Talks:

1. The generalized Tate diagrams of equivariant slice filtration. Young-Hom online seminar. Oct 2024.

2. THH of the p-adic integer. MIT Talbot. Aug 2024.

3. The generalized Tate diagrams of equivariant slice spectral sequences. MSU Graduate Student Topology and Geometry Conference. April 2024. 

4. Zero-pointed Manifolds: factorization homology. Graduate Student Topology Seminar at University of Notre Dame. Spring 2023.

5. Formal groups and Hopf algebroids. Graduate Student Topology Seminar at University of Notre Dame. Spring 2022.

6. Atiyah-Segal completion theorem. eCHT reading seminar. Spring 2022.

7. Motivic homotopy theory. Graduate Student Topology Seminar at University of Notre Dame. Fall 2019.

Seminars:

1. Equivariant homotopy theory, co-organizer: Jack Carlisle, Spring 2024. Graduate Student Topology Seminar at University of Notre Dame.