Jānis Lazovskis - Research

Profile picture of Janis Lazovskis Department of Mathematics, Statistics, and Computer Science
University of Illinois at Chicago

322 Science and Engineering Offices
851 South Morgan Street
Chicago IL 60607-7045
United States of America

SEO 522
jlazov2 (at) uic (dot) edu


This page contains research diretions I am currently involved in and have been involved in. The "Projects" section will hopefully be replaced by a "Publications" section, but right now contains different directions of math that I've explored. Most of the talks have linked notes that I used while giving the talks. A more up-to-date (but less organized) collection is my math blog.

Projects:
(2017) A constructible sheaf via universality over configuration spaces

Research with Ben Antieau. Related blog posts 1 and 2.

(2017) Extending persistent homology

Research with Ben Antieau and Shmuel Weinberger. Related blog posts 1 and 2.

(2016) Classical topological data analysis

UIC independent study with Ben Antieau. Related GitHub project, blog posts 1, 2, 3, 4, 5, and semester project.

(2016) Moduli spaces of Higgs bundles over Riemann surfaces

UIC independent study with Laura Schaposnik. Related blog posts 1, 2, 3, 4.

(2013 - 2014) Characterizations of the Chern characteristic classes

UW Master's project

(2012 - 2013) Undergraduate projects
     Algebraic and topological perspectives on the Khovanov homology

UW 2013 winter term independent study

     An isomorphism between the Hopf algebras of Jacobi diagrams in knot invariant theory

UW 2012 fall term independent study, based on D. Jackson's work

     Abstract tensor systems and diagrammatic representations

UW 2012 winter term independent study, based on D. Jackson's work


Seminars organized:
(Fall 2017) Infinity categories

UIC graduate learning seminar

(Fall 2013) Characteristic classes seminar

UW Algebraic Topology learning seminar


Talks:
(November 3rd and 10th, 2017) Coneability

UIC Hermanos seminar

(October 30th, 2017) Consructible sheaves and exit paths

UIC Infinity categories learning seminar

(October 9th, 2017) Analyzing topology with data

UIC Undergraduate Math Club

(September 20th, 2017) Geometric categories

UIC Graduate student Geometry and Topology seminar

(September 11th, 2017) Simplicial sets

UIC Infinity categories learning seminar

(September 8th, 2017) The Ran space and stratifications

UIC Groves geometric group theory seminar

(April 21st, 2017) Extending persistent homology

UIC Hermanos seminar

(February 24th, 2017) Serre duality on schemes

UIC Algebraic Geometry 2 lecture

(February 8th, 2017) Geodesic laminations, part 1

UIC Graduate student Geometry and Topology seminar

(November 30th, 2016) Finite point reconstruction

UIC Graduate student Geometry and Topology seminar

(November 18th, 2016) Calculations with the conditioning number

UIC Geometry and Topology day

(October 10th, 2016) Higgs bundles

UIC Groves geometric group theory seminar

(September 21st, 2016) Seifert fibered surfaces

UIC Graduate student Geometry and Topology seminar

(September 19th, 2016) Topological data analysis

UIC Graduate Student Colloquium

(September 7th, 2016) Your departmental website

UIC Special presentation on how to use departmental webspace

(March 30th, 2016) The Hodge diamond of hypersurfaces

UIC Algebraic geometry RTG reading seminar

(January 27th, 2016) Homotopy groups of spheres

UIC Graduate student Geometry and Topology seminar

(January 21st, 2016) Formal group laws and Lazard's theorem

UIC Chromatic Homotopy theory seminar

(November 30th, 2015) K3 surfaces

UIC Differentiable Manifolds final, with handout

(October 28th, 2015) Rational computations of K-theory

UIC Homotopy theory seminar

(October 21st, 2015) Geometric realizations (of rings)

UIC Graduate student Geometry and Topology seminar

(September 9th, 2015) A gentle introduction to sheaves

UIC Groves geometric group theory seminar

(March 17th, 2015) Grassmannians and group actions

UIC Groves Geometric group theory seminar

(February 11th, 2015) Milnor and Sullivan's results on bounded cohomology

UIC Graduate student Geometry and Topology seminar, based on this and this paper

(January 20th, 2015) Tiling the hyperbolic plane

UIC Groves Geometric group theory seminar

(November 19th, 2014) An introduction to knot contact homology

UIC Graduate student Geometry and Topology seminar, based on this paper

(October 15th, 2014) Presentations of the braid group

UIC Groves Geometric group theory seminar, based on this paper

(July 10th, 2014) The Khovanov homology

PIMS Presentation at the West Coast Algebraic Topology Summer School

(June 11th, 2014) Sheaf cohomology and manifolds

UW Algebraic geometry seminar, from a section of my master's project

(June 4th, 2014) TikZ and you: how to get the most out of code-generated graphics

UW Special presentation on how to use and harness TikZ, to Pure Math and C&O departments

(May 27th, 2014) A gentle introduction to knots and knot invariants

UW Joint Pure Math and C&O graduate student colloquium, basics and same invariants, mostly Vassiliev's and Khovanov's

(May 22nd, 2014) Complex submanifolds

UW Analysis seminar in several complex variables, with a geometric flavor

(May 13th, 2014) The CW-structure and cohomology of the complex Grassmannians

UW Geometry and Topology working seminar, from a section of my master's project

(April 3rd, 2014) A gentle introduction to moduli spaces

UW Pure Math graduate student colloquium, a taste of moduli spaces from several different areas of mathematics

(September 19th, 2013 - October 24th, 2013) Characteristic classes seminar

UW Algebraic Topology learning seminar, weekly talks

(March 20th, 2013) Flows and unique diffeomorphism classes

UW Geometry and Topology learning seminar on Morse theory


Conferences:
(July 30 - August 4, 2017) Topological Data Analysis: Developing Abstract Foundations

at the Banff International Research Station

(April 23-28, 2017) Applied and Computational Algebraic Topology Spring School

at the Hausdorff Research Institute for Mathematics, Bonn University

(October 21-23, 2016) Workshop on the geometry and physics of Higgs bundles

at the University of Illinois at Chicago

(August 8-13, 2016) West Coast Algebraic Topology Summer School

at the University of Oregon.
Prepared talk on complex bordism theory with Maximilien Holmberg-Péroux

(March 28-29, 2015) Graduate Student Topology and Geometry Conference

at the University of Illinois at Urbana-Champaign

(July 7-12, 2014) West Coast Algebraic Topology Summer School

at the University of British Columbia.
Prepared talk on Khovanov's knot homology with Robin Koytcheff



jlazovskis.com  |  mat-blag.blogspot.com

This page was last updated on 2017-11-06 at 19:26 CST