## Welcome to the web home of Papri Dey

## About me

I am a postdoc fellow in the Department of Mathematics, University of Missouri since June 2019, working under the supervision of Prof. Dan Edidin.

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 guest 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

Convex Algebraic Geometry : Monic Symmetric /Hermitian Determinantal Representations of Polynomials, Characterization of Spectrahedra, feasible sets of Semidefinite Programming, Semidefinite Representation of Convex Sets

Nonlinear Algebra

Computational Algebra

## Publications and Preprints

Papri Dey, and Harish K Pillai. A Complete Characterization of Determinantal Quadratic Polynomials,

*Linear Algebra and its Applications*543 pp. 106-124, 2018.Papri Dey. Definite Determinantal Representations of Multivariate Polynomials,

*Journal of Algebra and its Applications*2050129 pp. 1-29, 2020.Papri Dey, Paul Goerlach, and Nidhi Kaihnsa. Coordinate-wise Powers of Algebraic Varieties,

*Beitr Algebra Geom*(2020) doi:10.1007/s13366-019-00481-8 .Justin Chen, and Papri Dey. Computing symmetric determinantal representations,

*Journal of Software for Algebra and Geometry*, 10 pp. 9-15, 2020.Papri Dey, and Daniel Plaumann. Testing hyperbolicity of real polynomials,

*Math. Comput. Sci.*(2020) doi:10.1007/s11786-019-00449-w .Papri Dey. Definite Determinantal Representations via Orthostochastic Matrices,

*Journal of Symbolic Computation*(2020) doi:10.1016/j.jsc.2020.04.005Papri Dey, Stephan Gardoll, and Thorsten Theobald. Conic stability of polynomials and positive maps, J

*ournal of Pure and Applied Algebra*(2020) doi: 10.1016/j.jpaa.2020.106610.Justin Chen, and Papri Dey. The 4Ă—4 orthostochastic variety, preprint

**Software package: **

Justin Chen and Papri Dey.

DeterminantalRepresentations: A Macaulay2 package

I**n Preparation**:

Bit Complexity of Jordan Form, Spectral factorization, and Determinantal representation of Hyperbolic Polynomials, joint work with Ravi Kannan, Nick Ryder and Nikhil Srivastava.

Principal Matrices of Numerical Semigroups, joint work with Hema Srinivasan.

## Invited Seminars/Talks/Sessions

A Geometric Approach to Conic Stability of Polynomials. Reunion workshop on

**Geometry of Polynomials, Simons Institute, UC Berkeley, USA,**2020.Conic Stability of Polynomials.

**Data Seminar, University of Missouri, 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.**

## Contact

219 Math Sciences Building

810 East Rollins Street

Columbia, MO 65211 , USA

Email: yedirpap@gmail.com or pdbdn@missouri.edu