Artem’s webpage

Artem’s webpage

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Currently: research lead at cyber•Fund Previously: mathematician at Stony Brook Email: artofkot [ат] gmail.com, telegram: @artofkot

Artem’s blogArtem’s blogBlockchain courseBlockchain course
About me

2023-today: crypto-research lead at cyber•Fund

2013-2023: mathematician in the US (PhD in Princeton, then postdocs in Indiana University and Stony Brook).

2004-2013: math student in Moscow (high-school #57, then BA+MA in Lomonosov MSU).

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

Apart from crypto and math I also like game go (~1dan), chess, volleyball, table tennis. I also have some programming experience:

For more details, take a look at my CV

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:

Publications:

More:

  • Introductory talk about Heegaard Floer and Khovanov homologies ( video | slides )
  • Talk in Montreal, 2018 (notes)
Teaching
  • Blockchains: theory and applications (Blockchain courseBlockchain 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.

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, 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.”

I think that the single most valuable thing in this course was Artem's availability and willingness to meet and help with students. At any time, students always felt welcome to engage in a conversation with Artem about anything math, and especially our projects.

Artem was an amazing professor who brought an in depth knowledge of blockchain technology to lecture.

Artem is incredibly passionate about the subject matter and that was shown throughout his lectures.

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.”