Nilava Metya

About me

I am a second year graduate student in mathematics at Rutgers University. I'm quite social and you'll find me talking to lots of people in the department. I mostly interact with Arunesh Sinha and Guanyang Wang, among professors. Email me at nilava.metya@rutgers.edu if you have any question (about anything: life in general, the math community at Rutgers, ...)

Something I want to clarify for readers of this webpage: This is my professional webpage written from my personal point of view and I have different optinions on learning vs research. For me, learning includes research; I refer to learning from a book/paper/others as second-hand learning and learning from my own insights/research/results as first-hand learning. So if you see the word 'learn', it does include research sometimes.

My learning interests lie in applied areas of Distributionally Robust Optimization, Homotopy Continuation methods for optimization, MCMC methods, Graphical Models, Applied Algebraic Geometry and theoretical Machine Learning.
I love solving problems (and mathematical puzzles), especially those similar to olympiad style and competitive coding problems.

Here is a CV.

Goals to reach within 2023:

• Read some of algebraic statistics
• Gain a general understanding of actual statistics.

Goals to reach within 2024:

• Gain an understanding of optimization and apply algebra (not just linear algebra) to optimization
• Gain an understanding of Machine Learning (including implementation).

Goals to reach within 2028 (strict upper bound):

• Graduate with a PhD
• Join a supportive RnD or a research position (including academia and industry) to learn more about aspects of ML, optimization, and quantum computing, and use them in real-world problems.

Education

Activities

(Dec 2023) Bayesian Statistics and Statistical Learning: New Directions in Algebraic Statistics at IMSI, Chicago.

(Oct 2023) Algebraic Statistics for Ecological and Biological Systems at IMSI, Chicago.

(Oct 2023) Apprenticeship Week at IMSI, Chicago.

(Sep 2023) Algebraic Statistics and Applications at IMSI, Chicago.

(Aug 2023) Permutations and Causal Inference at IMSI, Chicgo.

(Jun 2023) Algebraic Methods in Biochemical Reaction Networks at MPI, Leipzig (organized by MPI Leipzig and SLMath).

(May 2023) Attending as the head counsellor at PROMYS India.

(Jan-Apr 2023) Organizing ANGeLS - the Algebra and Geometry Learning Seminar for graduate students. Please drop by at HILL 525 at 9AM every Wednesday to enjoy bagels over some wonderful talks on Quiver Representations.

Talks/Write-ups

1. Inference on growth process of a network at Rutgers for the course on Data Mining
   Reference Paper.
   Slides. Report. Video.


2. Principal Components along Quiver representations at Rutgers for the course on Topological Data Analysis
   Reference Paper: Principal Components along Quiver Representations.
   Slides.


3. Representations as sections of line bundles at Princeton for the course on Algebraic Geometry
   Notes.


4. Complexity of Optimization at Rutgers Math department Pizza Seminar
   Slides.


5. Quvier representations - geometry and invariants at Rutgers Algebra aNd GEometry Learning Seminar
   References: a geometric view.
   Notes.


6. Quvier representations at Rutgers Graduate Algebra and Representation Theory Seminar
   References: Quiver representations via reflection functors, a geometric view, beyond Dynkin quivers.
   Notes.


7. Burnside's p^aq^b theorem at Rutgers Graduate Number Theory Seminar
   Reference: Abstract Algebra by Dummit and Foote.


8. Kneser Graph Coloring at Rutgers Graduate Combinatorics Seminar
   Reference: A new short proof of Kneser's conjecture.


9. Very Basic Lie Theory at Rutgers Geometry and Topology Seminar
   Reference: Very Basic Lie Theory by Howe.


10. Well-definedness of the Brauer group at Rutgers Algebra aNd GEometry Learning Seminar
    Reference: Associative Algebras by Pierce.


11. Fiedler Vector Methodat CMI for the course on Matrix Computations
    These are the slides, written report, and video based of a group project on the Fiedler vector method - an approximate way to find a balanced graph cuts.
    Slides. Report. Video.


12. Cantor Set
    Here are the notes for a talk on Cantor set I gave in a tutorial in Graduate Analysis I course.
    Notes.


13. Markov Chain Monte Carlo
    This is the presentation based on an internship with Prof R V Ramamoorthi.
    Presentation.


14. Quantum Computing
    These are the write-ups for a series of four talks I gave at a PROMYS counsellor seminar on Quantum Computing.
    Talk 1. Talk 2. Talk 3. Talk 4.


15. Lie Algebras and their Representations
    These are the slides and the writeup for a series of talks I gave at a PROMYS counsellor seminar on Representation theory of Lie algebras.
    Writeup. Talk 1. Talk 2. Talk 3.


16. Introduction to Hyperbolic Geometry
    These are the write-ups for a series of four talks I gave at a PROMYS counsellor seminar on the calculus on the upper half plane in Hyperbolic geometry.
    Writeup.


17. Computer Project in grade 12
    These are the project writeups for my project for grade 12 in high-school. One is a compilation of codes we did throughout the year, another is a larger project to imitate a retail shop and implement an inventory of items.
    Compilation. Inventory.