## Research

My research mainly concerns a family of one-dimensional stochastic growth models known as the Kardar-Parisi-Zhang (KPZ) universality class, focusing on several perspectives on Gibbsian line ensembles, last passage percolation, and models with integrable or exactly solvable structure.

### Papers

- The lower tail of \(q\)-pushTASEP.

With Ivan Corwin.

*Communications in Mathematical Physics,*to appear. arXiv. Slides.

- Brownian structure in the KPZ fixed point.

With Jacob Calvert and Alan Hammond.

*Astérisque*, vol. 441 (2023). arXiv. Slides.

- Optimal tail exponents in general last passage percolation via bootstrapping & geodesic geometry.

With Shirshendu Ganguly.

*Probab. Theory Relat. Fields*, 186, no. 1–2, 221–284 (2023). arXiv. Slides.

- Local and global comparisons of the Airy difference profile to Brownian local time.

With Shirshendu Ganguly.

*Ann. Inst. H. Poincaré Probab. Statist.*, 59, no. 3, 1342--1374 (2023). arXiv. Slides.

- Exceptional times when the KPZ fixed point violates Johansson's conjecture on maximizer uniqueness.

With Ivan Corwin, Alan Hammond, and Konstantin Matetski.

*Electron. J. Probab.*, 28, no. 11, 1-81 (2023). arXiv. Slides.

- Interlacing and scaling exponents for the geodesic watermelon in last passage percolation.

With Riddhipratim Basu, Shirshendu Ganguly, and Alan Hammond.

*Commun. Math. Phys.*, 393, no. 3, 1241–1309 (2022). arXiv.

- Lower Deviations in \(\beta\)-ensembles and Law of Iterated Logarithm in Last Passage Percolation.

With Riddhipratim Basu, Shirshendu Ganguly, and Manjunath Krishnapur.

*Israel J. Math.*, 242, no. 1, pages 291–324, (2021). arXiv.

- Critical point for infinite cycles in a random loop model on trees.

With Alan Hammond.

*Ann. Appl. Probab.*, 29, no. 4, 2067–2088, (2019). arXiv. Slides.

### Preprints

- Brownian bridge limit of path measures in the upper tail of KPZ models.

With Shirshendu Ganguly and Lingfu Zhang.

*Submitted.*arXiv.

- Sharp upper tail estimates and limit shapes for the KPZ equation via the tangent method.

With Shirshendu Ganguly.

*Submitted.*arXiv. Slides.

### Expository writing

- Fractal structure in the directed landscape.

With Shirshendu Ganguly.

*For a special issue in honour of Rajeeva L. Karandikar.*We plan on expanding this in the future.

### Talks/Slides (same as above)

- The lower tail of \(q\)-pushTASEP.

- Understanding the upper tail behaviour of the KPZ equation via the tangent method.

- The Airy difference profile and Brownian local time.

- Fractal dimension of multiple maximizers in the KPZ fixed point.

- Bootstrapping to optimal tail exponents in last passage percolation.

- Brownian structure in universal KPZ objects.

- A phase transition in a random loop model on infinite trees.

### Thesis

Probabilistic and geometric methods in last passage percolation.