Artem’s webpage

Artem’s webpage

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:

Preprints:

Publications:

More:

  • Introductory talk about Heegaar Floer and Khovanov homologies ( video | slides )
  • Talk in Montreal, 2018 (notes)
Teaching
  • Blockchains: theory and applications (
    Blockchain course
    Blockchain course
    ) Stony Brook University, Fall ‘22
Graduate course on Khovanov homology ( videos | lecture notes ) Indiana University, Spring ‘21

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.

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, Fall ‘20
  • Linear Algebra and Applications ( lecture notes ) Indiana University, Spring ‘20
  • Linear Algebra with Applications ( lecture notes ) Princeton University, Spring ‘17 + Fall ‘16
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: