Papers

My papers on arXiv
My Google Scholar page
My MathSciNet profile

1. Compatibility of quantum trace map with quantum UV-IR map
   with Samuel Panitch
     in preparation
   
   
2. Quivers and BPS states in 3d and 4d
   with Piotr Kucharski, Helder Larraguivel, Pietro Longhi, Dmitry Noshchenko and Piotr Sulkowski
     in preparation
   
   
3. Skein traces from curve counting
   with Tobias Ekholm, Pietro Longhi and Vivek Shende
     in preparation
   
   
4. Knot lattice homology and q-series invariants for plumbed knot complements
   with Rostislav Akhmechet and Peter K. Johnson
     to appear on Quantum Topology [arXiv:2403.14461]
   
   
5. 3d quantum trace map
   with Samuel Panitch
     preprint [arXiv:2403.12850]
   
   
6. Branches, quivers, and ideals for knot complements
   with Tobias Ekholm, Angus Gruen, Sergei Gukov, Piotr Kucharski, Marko Stošić and Piotr Sułkowski
     Journal of Geometry and Physics 177 (2022), 104520 [journal | arXiv:2110.13768]
   
   
7. Inverted state sums, inverted Habiro series, and indefinite theta functions
     preprint [arXiv:2106.03942]
   
   
8. Cobordism invariants from BPS q-series
   with Sergei Gukov and Pavel Putrov
     Annales Henri Poincaré 22 (2021), 4173-4203 [journal | arXiv:2009.11874]
   
   
9. $\hat{Z}$ at large $N$: from curve counts to quantum modularity
   with Tobias Ekholm, Angus Gruen, Sergei Gukov, Piotr Kucharski and Piotr Sułkowski
     Communications in Mathematical Physics 396 (2022), 143-186 [journal | arXiv:2005.13349]
   
   
10. Rozansky-Witten geometry of Coulomb branches and logarithmic knot invariants
    with Sergei Gukov, Po-Shen Hsin, Hiraku Nakajima, Du Pei and Nikita Sopenko
      Journal of Geometry and Physics 168 (2021), 104311 [journal | arXiv:2005.05347]
    
    
11. Large color R-matrix for knot complements and strange identities
      Journal of Knot Theory and Its Ramifications 29 (2020), no. 14, 2050097 [journal | arXiv:2004.02087]
    
    
12. 3d-3d correspondence for mapping tori
    with Sungbong Chun, Sergei Gukov and Nikita Sopenko
      Journal of High Energy Physics 09 (2020), 152 [journal | arXiv:1911.08456]
    
    
13. Higher rank $\hat{Z}$ and $F_K$
      SIGMA 16 (2020), 044, 17 pages [journal | arXiv:1909.13002]
    
    

PhD Thesis

• 3-manifolds, q-series, and topological strings
    Caltech Thesis (2022) [CaltechTHESIS:05252022-010117961]
  
  

  

A piece of recreational mathematics

• Prague Clocks
  with Chan Bae, John Conway, Lukas Kohlhase
    The Mathematical Intelligencer 38 (2016), 37 [journal]
  
  

  

Mathematica files

• Zedhat: a Mathematica package for computation of $\hat{Z}$ for negative definite plumbed 3-manifolds (written by Nikita Sopenko in 2019)
    [Zedhat package | Example usage]
• Large-color R-matrix: computation of $\hat{Z}$ for braid-positive link complements, following arXiv:2004.02087
    [Notebook]
• Inverted state sums: computation of $\hat{Z}$ for braid-homogeneous link complements and more, following arXiv:2106.03942
    [Notebook]