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 directions 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.

(2017) A constructible sheaf via universality over configuration spaces

Research with Ben Antieau and Shmuel Weinberger. Related blog posts 1, 2, 3, 4, and conclusion.

(2017) Extending persistent homologyResearch with BA and SW. Related blog posts 1 and 2.

(2016) Classical topological data analysis

Algebraic and topological perspectives on the Khovanov homology

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

(2016) Moduli spaces of Higgs bundles over Riemann surfacesUIC independent study with Laura Schaposnik. Related blog posts 1, 2, 3, 4.

(2013 - 2014) Characterizations of the Chern characteristic classesUW Master's project

(2012 - 2013) Undergraduate projectsAlgebraic 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 theoryUW 2012 fall term independent study, based on David Jackson's work

Abstract tensor systems and diagrammatic representationsUW 2012 winter term independent study, based on DJ's work

(Spring 2018) Graduate Student Topology and Geometry Conference

Annual Midwestern US graudate student conference

(Fall 2017) Infinity categoriesUIC graduate learning seminar

(Fall 2013) Characteristic classes seminarUW Algebraic Topology learning seminar

(February 8th, 2018) Algebra and geometry on topological spaces: a new look at data

UIC Graduate Student Colloquium

(January 8th, 2018) Par doktorantūru ZiemeļamerikāLJZA zinātnieku tikšanās

(November 29th, 2017) Perspectives on the Ran space

UIC Graduate student Geometry and Topology seminar

(November 3rd and 10th, 2017) ConeabilityUIC Hermanos seminar

(October 30th, 2017) Consructible sheaves and exit pathsUIC Infinity categories learning seminar

(October 9th, 2017) Analyzing topology with dataUIC Undergraduate Math Club

(September 20th, 2017) Geometric categoriesUIC Graduate student Geometry and Topology seminar

(September 11th, 2017) Simplicial setsUIC Infinity categories learning seminar

(September 8th, 2017) The Ran space and stratificationsUIC Groves geometric group theory seminar

(April 21st, 2017) Extending persistent homologyUIC Hermanos seminar

(February 24th, 2017) Serre duality on schemesUIC Algebraic Geometry 2 lecture

(February 8th, 2017) Geodesic laminations, part 1UIC 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 numberUIC Geometry and Topology day

(October 10th, 2016) Higgs bundlesUIC Groves geometric group theory seminar

(September 21st, 2016) Seifert fibered surfacesUIC Graduate student Geometry and Topology seminar

(September 19th, 2016) Topological data analysisUIC Graduate Student Colloquium

(September 7th, 2016) Your departmental websiteUIC Special presentation on how to use departmental webspace

(March 30th, 2016) The Hodge diamond of hypersurfacesUIC Algebraic geometry RTG reading seminar

(January 27th, 2016) Homotopy groups of spheresUIC Graduate student Geometry and Topology seminar

(January 21st, 2016) Formal group laws and Lazard's theoremUIC Chromatic Homotopy theory seminar

(November 30th, 2015) K3 surfaces

UIC Differentiable Manifolds final, with handout

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

(October 21st, 2015) Geometric realizations (of rings)UIC Graduate student Geometry and Topology seminar

(September 9th, 2015) A gentle introduction to sheavesUIC Groves geometric group theory seminar

(March 17th, 2015) Grassmannians and group actionsUIC Groves Geometric group theory seminar

(February 11th, 2015) Milnor and Sullivan's results on bounded cohomologyUIC Graduate student Geometry and Topology seminar, based on this and this paper

(January 20th, 2015) Tiling the hyperbolic planeUIC 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 groupUIC Groves Geometric group theory seminar, based on this paper

(July 10th, 2014) The Khovanov homologyPIMS Presentation at the West Coast Algebraic Topology Summer School

(June 11th, 2014) Sheaf cohomology and manifoldsUW 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 graphicsUW 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 invariantsUW Joint Pure Math and C&O graduate student colloquium, basics and same invariants, mostly Vassiliev's and Khovanov's

(May 22nd, 2014) Complex submanifoldsUW Analysis seminar in several complex variables, with a geometric flavor

(May 13th, 2014) The CW-structure and cohomology of the complex GrassmanniansUW Geometry and Topology working seminar, from a section of my master's project

(April 3rd, 2014) A gentle introduction to moduli spacesUW 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 classesUW Geometry and Topology learning seminar on Morse theory

(February 19-23, 2018) Linking Topology to Algebraic Geometry and Statistics

at the Max Planck Institute for Mathematics in the Sciences

Delivered poster talk about current research

at the Banff International Research Station

(April 23-28, 2017) Applied and Computational Algebraic Topology Spring Schoolat the Hausdorff Research Institute for Mathematics, Bonn University

(October 21-23, 2016) Workshop on the geometry and physics of Higgs bundlesat the University of Illinois at Chicago

(August 8-13, 2016) West Coast Algebraic Topology Summer Schoolat the University of Oregon.

Prepared talk on complex bordism theory with Maximilien Holmberg-Péroux

at the University of Illinois at Urbana-Champaign

(July 7-12, 2014) West Coast Algebraic Topology Summer Schoolat the University of British Columbia.

Prepared talk on Khovanov's knot homology with Robin Koytcheff

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This page was last updated on 2018-02-11 at 23:24 CST