What's new?
Completed the chapter on Newtonian-Sobolev functions @YoungMeasures: Link here.
Esmayli Behnam, Rajala Kai: Conformal Uniformization of domains bounded by quasitripods, https://arxiv.org/abs/2401.08485 (Jan 2024)
I have added many videos on Newtonian-Sobolev functions to @YoungMeasures.
I am teaching one course (business calculus) in Spring 2024. I have some new ideas in calculus teaching that I am trying out on (poor) them!
I taught two courses during Fall 2023. It was tough and took me time to figure the workings out, but came on top!
My Postdoc at University of Jyvaskyla ended Sept 25. I have started as VAP at University of Cincinnati, OH.
I have started Analysis on Metric Spaces video series on YouTube: https://youtu.be/NKIIKzlYznI
I have had to cancel my registration for the big conference in Helsinki in August (in honor of Mario Bonk). That is sad :( But I plan, at least for now, to join the summer school here in Jyvaskyla. David Bates will give some lectures.
Japan, Okinawa was very nice! Great trip, great mathematics, great people.
Conference: Potential theory and random walks in metric spaces, Okinawa Institute of Science and Technology, Okinawa, Japan. May 30-June 2, 2023. I will give a talk.
Conference: Metric Analysis, Parametrizations, and Surfaces (MAPS), University of Fribourg, Switzerland, 13. - 15. April 2023
Very excited about teaching a graduate complex analysis 2 course beginning in March 2023. Have been preparing intensely!
Talk at AMS Eastern Sectional Meeting coming up: Special Session on Quasiconformal Analysis and Geometry on Metric Spaces, I
Applying for jobs that begin in Fall 2023. See my updated teaching portfolio.
Talk: Nov 30, Analysis Seminar, University of Jyväskylä on this paper of mine with (Piotr Hajlasz): "Lipschitz mappings, metric differentiability, and factorization through metric trees (arXiv:2106.15763)"
Talk at BIRS conference (Canada) on Nov 25. Coarea inequality for sobolev functions on metric surfaces
Coarea Inequality for Monotone Functions on Metric Surfaces, Behnam Esmayli, Toni Ikonen, Kai Rajala, now on arxiv here.
Paper with Piotr Hajlasz, Lipschitz mappings, metric differentiability, and factorization through metric trees (arXiv:2106.15763) is accepted in the Journal of the London Mathematical Society
Geometric Measure Theory book review: PDF here and video here.
Chapter on Coarea Formula is completed on my YouTube channel. Direct link .
On my YouTube channel : area formula (GMT).
Talk: Analysis Seminar at University of Jyväskylä, Dec 15, in-person and on Zoom. Title: Weighted coverings and the Hausdorff measure (Slides from the talk)
Talk: Wednesday November 17, Analysis Seminar at the University of Tennessee, Knoxville. On equivalent assumptions in the (metric) implicit function theorem, Organizer: Vyron Vellis
In-person conference, Aalto University, October 27–29, 2021. Conference website: http://math.aalto.fi/conferences/agent2021/
My thesis is now freely available on Pitt website: http://d-scholarship.pitt.edu/41368/ (PhD thesis: Geometric Function Theory in Metric Spaces, 2021)
Everything I touch these days leads to fat Cantor sets and maps with low rank, or those that factor through a tree!
In Finland -- finally! It was a lengthy process to have all immigration formalities in place, but we made it. I love my office and everyone here is so warm and welcoming. Looking forward to a good start.
Received my AMS vest from the MRC I joined in June :) It is quite dull in color, but... I am happy I got it.
New paper on ArXiv: Lipschitz mappings, metric differentiability, and factorization through metric trees, Behnam Esmayli, Piotr Hajłasz, 2021
I am excited for a Postdoc offer at the University of Jyväskylä (Finlan). I will begin September 2021.
I just defended my thesis at the University of Pittsburgh -- June 30! Here are my presentation slides.
I have launched my YouTube channel where I solve advanced calculus/analysis problems. Please SUBSCRIBE!
My collection of advanced calculus problems is growing!
Check out my two PDF's on Hessian Matrix and Multivariable Taylor's Theorem that I prepared for an advanced calculus course that I TA for.
As a member of math Graduate Student Organization, I am helping resume the graduate seminars beginning Monday 2/15.
Gave a talk on 2/11/2021 that was basically a survey of area and coarea formulas for metric target spaces. Slides here.
Working on a functional $H^{2,m}(f,A)$ where $f:R^n \to X$ is Lipschitz and $A$ is a subset of domain so that $H^{2,m}(f,A)=0$ implies that $f$ factors through a metric tree. This has connections to the coarea inequality and coarea formula.
(Ongoing) I am a participant in AMS MRC, Analysis on Metric Spaces, June 13 – 19, 2021 (Initially planned for summer 2020, there are currently active meetings every month, see schedule here.) Topics I have enjoyed learning about so far: first order calculus on metric measure spaces, quasiconformal maps.
Working on coarea formula both in Euclidean and in metric space setting. Despite being a classical result, many interesting questions come up once you dig deeper! These days I wonder what the simplest pat to the proof of the coarea formula in Euclidean space might be!
Applying for (academic) jobs! Wish me luck.