Deepam Patel
Associate Professor of Mathematics and Director of Online Programs, College of Sciences
Purdue University
West Lafayette, IN 47907

Office: Math 606
E-mail: patel471 "at" purdue "dot" edu
Phone: 765-494-1966

---

I am an Associate Professor of Mathematics and Director of Online Programs in the College of Science at Purdue University. I lead College participation in university-wide online graduate initiatives, including the pan-Purdue M.S. in Artificial Intelligence and M.S. in Data Science. My research spans algebraic geometry and number theory, with recent work at the interface of logic/VC density and data-driven methods. I am actively interested in AI for mathematics (LLM-assisted reasoning, formal methods) and quantitative modeling.

---

Teaching (Fall 2025):

M598: Applied Etale Cohomology

M351: Elementary Linear Algebra
Note: All course information for M351 is available through your course Brightspace page.

---

Research : I'm mostly interested in algebraic geometry/number theory. More recently, I've become interested in some aspects of model theory, logic, and AI for mathematics. You can find more information and some papers/preprints here.

Selected Publications:

• De Rham epsilon factors. (pdf)
  Inventiones Mathematicae, Vol. 190, No. 2, 2012, pp. 299-355. 
  
• Motivic structure on higher homotopy of hyperplane arrangements. (pdf)
  Mathematische Annalen, 366(1), 2016, pp. 279-300.
  
• Lefschetz theorems for torsion algebraic cycles in codimension 2. (pdf)
        With G.V. Ravindra.
  Advances in Math., 315, 2017, pp. 554-575.
• Locally analytic representations of GL(2) via semistable models of P^{1}. (pdf)
        With Tobias Schmidt and Matthias Strauch.
  Journal of the Institute of Math. of Jussieu, 18, No. 2, 2019, pp. 125-187.
• VC Density of definable families over valued fields (pdf)
        With Saugata Basu.
  Journal of the European Mathematical Society, Vol. 73, No. 7, 2021, pp. 2361-2403.
  
• Nonnegativity of Signed Euler Characteristics of Moduli of Curves and Abelian Varieties. (pdf)
        With D. Arapura
  Mathematische Annalen, 394, 2026
  
• Local Monodromy of Constructible Sheaves. (pdf)
        With M. Nori,
       to appear, Crelle
  

---

Algebraic Geometry Seminar: see here for more information.

---

Learning Seminar:

Most semesters, I and some members of the algebraic geometry/number theory group organize some sort of learning seminar.

Spring 2025: Condensed Mathematics (see here).

Fall 2024:The Weil Conjectures, see here for more information.

Fall 2021: We (Tong Liu, Dan Le, Shiang Tang) organized a learning seminar on Mazur's Eisenstein Ideal Paper, see here for more information.

---