## Welcome to the web home of Papri Dey

## About me

I am a Visiting Assistant Professor in the School of Mathematics at Georgia Tech. My mentor is Prof. Greg Blekherman.

Before that I was a postdoc fellow in the Department of Mathematics, University of Missouri-Columbia from June 2019 to June 2022. I completed my PhD in June 2017 under the supervision of Prof. Harish K. Pillai in the Department of Electrical Engineering, Indian Institute of Technology (IIT) Bombay. In my PhD thesis, I worked on Determinantal Representations of Multivariate Polynomials that is considered as one of the fundamental problems in Convex Algebraic Geometry. I worked as a visiting scientist in Max Planck Institute for Mathematics in the Sciences, Leipzig under the supervision of Prof. Bernd Sturmfels from October 2017 to January 2018, and as a visiting scientist in the R. C. Bose centre for Cryptology and Security, Indian Statistical Institute (ISI), Kolkata under the supervision of Prof. Bimal K. Roy during March - August, 2018. Then I spent Fall 2018 as a postdoc at Brown University in the Institute for Computational and Experimental Research in Mathematics (ICERM) during the semester program on nonlinear algebra, worked under the supervision of Prof. Jonathan Hauenstein and spent Spring 2019 as a Microsoft Research Fellow at Simons Institute for the Theory of Computing, University of California, Berkeley during the semester program on geometry of polynomials under the mentorship of Prof. Alistair Sinclair .

## Research Interests

My research interests lie in the intersection of algebra, geometry, and combinatorics, with far-reaching applications in optimization, theoretical computer science, and data science.

Convex Algebraic Geometry

Nonlinear Algebra

Algebraic Combinatorics

## Publications

Papri Dey, and Harish K Pillai. A Complete Characterization of Determinantal Quadratic Polynomials, Linear Algebra and its Applications 543, 106-124, 2018.

Papri Dey. Definite Determinantal Representations of Multivariate Polynomials, Journal of Algebra and its Applications 2050129 , 1-29, 2020.

Papri Dey, Paul Goerlach, and Nidhi Kaihnsa. Coordinate-wise Powers of Algebraic Varieties, Beitr Algebra Geom 61, 473-505 2020.

Justin Chen, and Papri Dey. Computing symmetric determinantal representations, Journal of Software for Algebra and Geometry 10, 9-15, 2020.

Papri Dey, and Daniel Plaumann. Testing hyperbolicity of real polynomials, Mathematics in Computer Science. 14, 111-121, 2020.

Papri Dey. Definite Determinantal Representations via Orthostochastic Matrices, Journal of Symbolic Computation 104, 15-37, 2021.

Papri Dey, Stephan Gardoll, and Thorsten Theobald. Conic stability of polynomials and positive maps, Journal of Pure and Applied Algebra 225, 106610, 2021.

Justin Chen, and Papri Dey. The 4×4 orthostochastic variety, Experimental Mathematics (2020).

Papri Dey, and Hema Srinivasan. Principal matrices of numerical semigroups , WICA Book Chapter, Springer, AWMS, Vol-29, 2021 .

Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava. Bit Complexity of Jordan Normal Form and Spectral Factorization , ITCS 2023, volume LIPIcs, Volume 251.

## Preprints

Papri Dey. Real Degeneracy loci of matrices and Phase Retrieval (submitted).

Papri Dey. Polynomials With Lorentzian Signature and Computing Permanents (https://arxiv.org/abs/2206.02759).

## Software package

Justin Chen and Papri Dey.

DeterminantalRepresentations: A Macaulay2 package

## In Preparation

Polynomials with Lorentzian Signature over Convex Cones, joint work with Greg Blekherman (mentor, GT).

Characterizing Matrices with zero kxk principal minors, joint work with Greg Blekherman (mentor, GT) and Abeer Al-Ahmadieh (GT).

## Invited Seminars/Talks/Sessions/Workshop

Algebra Seminar, Georgia Tech, January 29, 2024.

JMM 2024, on Topological and Algebraic Approaches for Optimization at San Francisco, CA, January 3-4, 2024.

Discrete Math Seminar, Kennesaw State University, November 29, 2023.

Convexity mini-symposium at the SIAM Conference on Applied Algebraic Geometry, July 10-14, 2023.

MAAG 2023 at Georgia Institute of Technology, April 15-16, 2023.

Algebraic Methods in Algorithms, special session at the AMS Spring Southeastern Sectional Meeting, March 18-19, 2023 at GT.

An Introduction to Nonlinear Algebra, Research Horizons Seminar, SoM at Georgia Tech, November 9, 2022.

Optimization and Data Science Seminar at UCSD, October 12, 2022.

Computational and Applied Algebraic Geometry, a special session at the AMS Central Sectional Meeting at Purdue University, March 26-27, 2022.

Applied Algebra Seminar at UW Madison, December 2, 2021.

Colloquium at IISc Math, November 16, 2021.

Real Polynomials: Counting and Stability workshop in Oaxaca, October 17- 22, 2021.

Convex Algebraic Geometry mini-symposium at the SIAM Conference on Applied Algebraic Geometry, August 16-20, 2021.

Lightning talks, ICERM Workshop Geometry and Combinatorics from Root Systems (Mar 22 - 26, 2021), Brown University, USA.

Optimization and Real Algebraic Geometry special session at AMS Spring Southeastern Sectional Meeting, March 13-14, 2021.

Real Degeneracy loci of matrices and their configurations, AWM chapter seminar, University of Pittsburgh, USA, March-2021.

Lightning talks, ICERM Workshop Sage/Oscar Days for Combinatorial Algebraic Geometry (Feb 15-19, 2021), Brown University, USA.

An Introduction to Nonlinear Algebra. AWM Lunch Talk, University of Missouri-Columbia, USA, Feb-2021.

A Geometric Approach to Conic Stability of Polynomials. Reunion workshop Geometry of Polynomials, Simons Institute, UC Berkeley, USA, 2020.

Conic Stability of Polynomials. Data Seminar, University of Missouri-Columbia, USA, 2020.

Computing Definite Determinantal Representations of Helton-Vinnikov Curves. KUMUNU 2019, University of Nebraska, Lincoln, USA, Plenary speaker.

Computing Definite Determinantal Representations of Helton-Vinnikov Curves. Algebra Seminar, University of Missouri -Columbia, USA, 2019.

Solving polynomial systems in Julia, MSRI, UC Berkeley, USA, workshop, 2019.

One of two organizers for weekly Open Problem session at Simons Institute, UC Berkeley, 2019.

A Computational Relaxation to Determinantal Representation Problem: Algebraic Combinatorial Approach, Simons Fellows talk, Simons Institute for the Theory of Computing, UC Berkeley, USA, 2019.

A Knot between Convex Algebraic Geometry and Non-linear Algebra. Post-doc seminar, ICERM, Brown University, USA, 2018

Characterization of determinantal Bivariate Polynomials. Geometrie TAG 2017, Otto-Von Guericke university, Magdeburg, Germany.

Monic symmetric/Hermitian determinantal representations of multivariate polynomials.TU Dortmund, Germany, seminar on Algebra and Geometry, 2017.

Monic symmetric/Hermitian Determinantal Representations of Multivariate Polynomials. Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, seminar on non-linear algebra, 2017.

## Course(s) taught

Math 2552-Differential Equations-Fall 2023 (Georgia Tech)

Math 2550-Intro. to Multi. Calculus -Spring 2022 (Georgia Tech)

Math 2552-Differential Equations-Fall 2022 (Georgia Tech)

Math 4100/7100- Differential Equations-Fall 2019, Spring 2020, Fall 2020 (Univ. of Missouri, Columbia)

Math 4720-Introduction to Abstract Algebra-Spring 2021 (Univ. of Missouri, Columbia)

Math 1700-Calculus 2-Fall 2021 (Univ. of Missouri, Columbia)

## Academic Services

Topological and Algebraic Approaches for Optimization

AMS Special Session on Combinatorics in Geometry of Polynomials,

Florida State University in Tallahassee, FL, March 23-24.

### Algebra Seminar Organizer (SoM, GT)

Here is the Schedule to Fall 2022 Algebra Seminar

Reviewer

AMS Math; Mathematics of Control, Signals, and Systems.

# Contact

019 Skiles Classroom Building

686 Cherry St NW

Atlanta, GA 30332 , USA

Email: yedirpap@gmail.com, or papri.dey@math.gatech.edu