Contact:gyan@nd.edu

Research Interests:

• I'm thinking about stuff related to the slice spectral sequence of BP_R^{C_{2^n}}, especially the generalized Tate diagrams of the slice spectral sequences with XiaoLin Danny Shi and Yutao Liu. 

• I'm thinking about global and equivariant formal group laws with Jack Carlisle, Yutao Liu, Noah Wisdom and Ryan Quinn.

• I am thinking about equivariant power operations with Noah Wisdom, Preston Cranford, and Hari Rau-Murthy.

Publications and Preprints:

1. The RO(C_{2^n})-graded homotopy of HZ through generalized Tate squares. Submitted. (arxiv, 2022) 

2. The RO(C_{2^n})-graded homotopy of HF_2. Submitted. (arxiv, 2023)

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

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

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

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

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

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

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

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

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

Contributed Talks:

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

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

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

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

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

Seminars:

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