Hi, we like and do mathematics, in Stony Brook.

Email: artofkot [ат] gmail.com

**Math research**

My work is at the intersection of symplectic geometry and low-dimensional topology. I use methods from bordered Heegaard Floer homology and Fukaya categories to study invariants of such objects as 3-manifolds, knots, mapping classes of surfaces.

In particular, these methods yield geometric invariants of 4-ended tangles, in the form of immersed curves on the boundary 4-punctured sphere. Currently, I think about knot theoretic applications of these immersed curve invariants, in the context of Khovanov, Heegaard Floer and instanton Floer theories. Take a look at my ** research statement** and papers below for more details.

### Teachers and collaborators:

Taras Panov (undergraduate adviser), Zoltán Szabó (PhD adviser), Claudius Zibrowius, Liam Watson, Tye Lidman, Allison Moore, Paul Kirk, Guillem Cazassus, Chris Herald.

### Preprints:

( video | slides )*Immersed curves in Khovanov homology***The correspondence induced on the pillowcase by the earring tangle**( video | slides )**Khovanov multicurves are linear****Cosmetic operations and Khovanov multicurves****Thin links and Conway spheres****Khovanov invariants via Fukaya categories: the tangle invariants agree**

### Publications:

To appear in Algebraic & Geometric Topology.**A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence****Khovanov homology and strong inversions**To appear in The Open Book Series.**Bordered theory for pillowcase homology**Mathematical Research Letters 26(5), 1467-1516.Michigan Mathematical Journal 30(3), 503-560.**Comparing homological invariants for mapping classes of surfaces**Journal of Symplectic Geometry 14(2), 431-448.**Minimal and Hamiltonian-minimal submanifolds in toric geometry**

### More:

*Introductory talk about Heegaar Floer and Khovanov homologies*( video | slides )*Academic CV*

**Teaching**

**Blockchains: theory and applications**() Stony Brook University, Fall ‘22Blockchain course

*( videos | lecture notes ) Indiana University, Spring ‘21*

**Graduate course on Khovanov homology**This course is an introduction to modern cut-and-paste techniques in knot theory, with a focus on Khovanov homology. Namely, we learn how Khovanov homology changes if one substitutes one 4-ended tangle in a knot with another. Examples of such an operation are Conway mutation and crossing changes.

Here are the main references we use: definition of Khovanov homology, s-invariant, Khovanov homology for tangles, Lagrangian Floer homology for curves, Khovanov homology for tangles via immersed curves.

We cover all this material from a modern viewpoint, using the latest developed algebraic tools. But no special background is needed, all the needed homological algebra is introduced.

**Calculus I**( lecture notes ) Indiana University, Spring ‘20**Linear Algebra and Applications****Linear Algebra with Applications**

**Evaluations I am most proud of:**

*“Overall, Dr. Kotelskiy is the best math teacher I have ever had”*

*“Artem is incredibly knowledgeable and is a great math professor.”*

*“Artem is enthusiastic about mathematics, and he wants his students to be as well. I believe that this is the best attribute of any instructor.”*

*“I thought Artem was a great person and cared a lot about the course.”*

*“I enjoyed his teaching style and how easily accessible Artem was after class. He would respond quickly to emails and would be very helpful during his office hours.”*

Interestingly, the following evaluation was as enjoyable to read as the ones above.
*“He doesn't curve the whole class after an exam just so he can get the class average he wants. You're rewarding students who didn't take the time to study as hard as the top students. I have never had a teacher tell students to drop the class as much as Artem. Every other class period after the first exam he kept telling us when the drop date was and when it got closer he just kept saying "You need to strongly think about dropping the class". He is not a motivator at all i.e. you're not a Professor. You're just an asshole who knows a lot about math.”*

**About me**

**2013-today:** doing math in the US (PhD in Princeton, then postdoc in Indiana University, then in Stony Brook).

**2004-2013:** studied math in Moscow (high-school #57, then Lomonosov MSU).

**1991**: born in Yerevan, on the same day when Armenia declared its independence from the USSR.

Apart from math I am also into blockchains, game go (~1dan), chess, volleyball, table tennis. I also have some programming expirience:

- Built (with Alex) an online platform for learning math; source code.
- Implemented a python package to work with type DA bimodules.