# Vaibhav Karve

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Name in Devanagari: वैभव कर्वे Name in IPA: ʋəibʱəʋə kərʋeː

I am a PhD candidate at the Department of Mathematics at the University of Illinois at Urbana-Champaign. My PhD advisor is Anil Hirani.

My research interests lie in graph theory, logic, algorithms and computational
topology. I am currently writing my doctoral thesis, titled *Graphical
structure of unsatisfiable boolean formulae* which combines the tools of graph
theory and topology to analyze boolean satisfiability – a classic problem in
logic and computer science.

I am also looking to extend my doctoral work towards the upcoming and adjacent field of computer-assisted formalized mathematics and interactive theorem proving (in particular, with the Lean theorem prover).

## Research

List of journal publications

2021 **Karve**, Yager, Abolhelm, Work, SowersSeasonal Disorder in Urban Traffic Patterns: A Low Rank Analysis 2020 **Karve**, HiraniThe complete set of minimal simple graphs that support unsatisfiable 2-CNFs 2017 Wu, Shindnes, **Karve**, Yager, Work, Chakraborty, SowersCongestion Barcodes: Exploring the Topology of Urban Congestion Using Persistent Homology These publications are also listed at UIUC math and Google scholar.

- Graph satisfiability
^{1} - Model theory in Lean
- Axiomatic geometry in Lean
- Manhattan traffic
- Past projects
- On the pullback of real exterior forms
- Congestion barcodes

## Teaching

My ever-evolving teaching philosophy.

**Currently teaching:**Spring 2021 Math 241 (Calculus III)- Math490: Computational mathematics
- Merit program @ Math UIUC
- Model theory in Lean @ Illinois Geometry Lab
- LeanTeach 2020 @ Illinois Geometry Lab + UniHigh Summer program
- Classical constructions @ Summer Illinois Math Camp, UIUC
Past courses

2021 Spring TA **Math 241**(*Merit*) Calculus III2020 Fall RA supervisor: Anil N. Hirani 2020 Spring TA **Math 490**Computational Mathematics2019 Summer RA Dabid G. Bourgin Fellow 2019 Spring TA **Math 490**Computational Mathematics2019 Fall RA supervisor: Anil N. Hirani 2018 Spring RA supervisor: Richard Sowers 2018 Fall TA **Math 285**(*Merit*) Intro to differential equations + Merit TA mentor2017 Summer RA supervisor: Richard Sowers 2017 Spring TA **Math 231**(*Merit*) Calculus II2017 Fall TA **Math 241**(*Merit*) Calculus III + Merit TA mentoring2016 Spring TA **Math 241**Calculus III2016 Fall TA **Math 221**(*Merit*) Calculus I2015 Fall TA **Math 241**Calculus III

## Notes

These are mostly notes I have taken as part of self-studying various things. They are not meant to be comprehensive notes – just a collection of things I found interesting at different times and wished to keep a record of.

- Algebraic geometry
- Algebraic topology
- Boolean satisfiability
- Category theory and haskell
- Combinatorial vector fields
- Coq
- Esperanto
- Geometry
- Git workflow
- Haskell
- Homology
- How I set up this website
- followed the steps here,
- also set up the sitemap.

- Lambda calculus
- Linear programming
- Logic
- Lua
- Mathematical tidbits
- Model theory
- Persistent homology
- Philosophy
- Python data model
- Python multiprocessing
- Python sqlite3
- Python's type theory
- Satisfiability ala Knuth
- Theory of computation
- Type theory

## Everything else

- 6174 : Kaprekar's constant visualized
- My areas of interest according to the Mathematics Subject Classification
- Plots and graphs I generated
- First attempt at publishing package : multihypergraph on PyPI
- Recognizing patterns in New York traffic : 4 min video as part of UIUC Graduate College's Research Live! 2016 competition.
- Slides from my talks
- Photos from conferences
- My Klein bottle
- My Goodreads profile

## Footnotes:

^{1}

this work was funded in Fall 2020 by the David G. Bourgin Mathematics Fellowship.