Matthew Badger | Department of Mathematics | University of Connecticut
Matthew Badger

Matthew Badger
University of Connecticut
Department of Mathematics
341 Mansfield Road, U-1009
Storrs, CT 06269-1009

Office: Monteith 326
Email: firstname.lastname _at_ uconn.edu

Spring 2019 Office Hours
M 1:30-2:30
Tu By Appointment
W 11:00-12:00
Th By Appointment
F Bu Appointment

Office hours are held in
Monteith 326

Geometry of Sets and Measures

I am an Assistant Professor of Mathematics at UConn (Associate Professor of Mathematics starting Fall 2019). I study the geometry of sets and measures using a mixture of geometric measure theory, harmonic analysis and quasiconformal analysis.

harmonic measure of a subset of the spherea quasicirclea 1-rectifiable measure

Quick Links: [Curriculum Vitae | Teaching | Research]

Analysis at UConn

In Spring 2019, the Analysis and Probability Seminar meets Fridays at 1:30pm. This is a research seminar featuring speakers from around the world. Organized by Scott Zimmerman.

In Spring 2019, we are continuing the Analysis Learning Seminar. Meeting time for Spring 2019 is Fridays 3:30-4:30. This seminar will primarily feature introductory talks by UConn graduate students and postdocs. All graduate students and advanced math majors who are interested in analysis, geometry, and probability are welcome to attend! Organized by Murat Akman and Vyron Vellis

Recent and Upcoming Events

2019 Northeast Analysis Network

2019 Northeast Analysis Network: September 21-22, 2019.

Geometric and Harmonic Analysis: a Conference for Graduate Students: March 29-31, 2019.

Nonsmooth Analysis: a Workshop for Postdocs: November 9-11, 2017.

[Archive of Past Events]

Teaching

[Math Course Schedules: Current Semester]

Spring 2019

Math 2710W, Section 3: Transitions to Advanced Mathematics

Math 3151, Section 1: Analysis II

Previous Semesters

Current PhD Students

Lisa Naples

I am happy to advise Ph.D. students who would like to carry out research at the interface of analysis and geometry.

Research

A non-technical description of my research with Raanan Schul on rectifiable measures can be found here.

Here is a picture related to my "Harmonic polynomials..." and "Flat points..." papers. The zero sets of homogeneous harmonic polynomials in x,y,z of odd degree may separate space into two components (cross your eyes to see a stereographic picture):

Intersecting Varieties

500x4y-1000x2y3+100y5 -5(x4+y4)z+10(x2+y2)z3+2z5=0 intersecting the unit sphere

Grants and Fellowships

NSF DMS 1650546
Analysis Program. CAREER Award. 2017 – 2022
NSF DMS 1500382
Analysis Program. Standard Grant. 2015 – 2018
NSF DMS 1203497
2012 NSF Mathematical Sciences Postdoctoral Research Fellowship

Publications and Preprints

[Statistics] Newest preprints/papers are listed first.

Regularity of the singular set in a two-phase problem for harmonic measure with Hölder data
(arXiv:1807.08002)
(with Max Engelstein and Tatiana Toro)
[Click to Show/Hide Abstract]
Status: accepted. To appear in Rev. Mat. Iberoam.
Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem
(arXiv:1806.01197 | Published Version)
(with Lisa Naples and Vyron Vellis)
[Click to Show/Hide Abstract]
Citation: M. Badger, L. Naples, V. Vellis, Hölder curves and parameterizations in the Analyst's Traveling Salesman theorem, Adv. Math. 349 (2019), 564-647. doi:10.1016/j.aim.2019.04.011
Generalized rectifiability of measures and the identification problem
(arXiv:1803.10022 | Published Version)
[Click to Show/Hide Abstract]
Note: This survey paper is based on a talk at the Northeast Analysis Network Conference held in Syracuse, New York in September 2017.
Citation: M. Badger, Generalized rectifiability of measures and the identification problem, Complex Anal. Synerg. 5 (2019), 2.
Geometry of measures in real dimensions via Hölder parameterizations
(arXiv:1706.07846 | Published Version)
(with Vyron Vellis)
[Click to Show/Hide Abstract]
Citation: M. Badger, V. Vellis, Geometry of measures in real dimensions via Hölder parameterizations, J. Geom. Anal. 29 (2019), no. 2, 1153-1192. doi:10.1007/s12220-018-0034-2
Multiscale analysis of 1-rectifiable measures II: characterizations
(arXiv:1602.03823 | Published Version)
(with Raanan Schul)
[Click to Show/Hide Abstract]
Citation: M. Badger, R. Schul, Multiscale analysis of 1-rectifiable measures II: characterizations, Anal. Geom. Metr. Spaces 5 (2017), no. 1, 1-39.
Related: H. Martikainen and T. Orponen (arXiv:1604.04091) have constructed a finite measure in the plane with bounded density-normalized L2 Jones function and vanishing lower 1-density. This implies that our use of β** in Theorem D is sharp and answers a question we posed following Theorem E.
Structure of sets which are well approximated by zero sets of harmonic polynomials
(arXiv:1509.03211 | Published Version)
(with Max Engelstein and Tatiana Toro)
[Click to Show/Hide Abstract]
Citation: M. Badger, M. Engelstein, T. Toro, Structure of sets which are well approximated by zero sets of harmonic polynomials, Anal. PDE 10 (2017), no. 6, 1455-1495.
Rectifiability and elliptic measures on 1-sided NTA domains with Ahflors-David regular boundaries
(arXiv:1507.02039 | Published Version)
(with Murat Akman, Steve Hofmann, and José María Martell)
[Click to Show/Hide Abstract]
Citation: M. Akman, M. Badger, S. Hofmann, J.M. Martell, Rectifiability and elliptic measures on 1-sided NTA domains with Ahlfors-David regular boundaries, Trans. Amer. Math. Soc. 369 (2017), no. 8, 2017, 5711-5745.
Two sufficient conditions for rectifiable measures
(arXiv:1412.8357 | Published Version)
(with Raanan Schul)
[Click to Show/Hide Abstract]
Citation: M. Badger, R. Schul, Two sufficient conditions for rectifiable measures, Proc. Amer. Math. Soc. 144 (2016), 2445-2454.
Local set approximation: Mattila-Vuorinen type sets, Reifenberg type sets, and tangent sets
(arXiv:1409.7851 | Published Version)
(with Stephen Lewis)
[Click to Show/Hide Abstract]
Note: The arXiv version of the paper has outdated numbering. The published version is open access and is the authoritative version.
Citation: M. Badger, S. Lewis, Local set approximation: Mattila-Vuorinen type sets, Reifenberg type sets, and tangent sets, Forum Math. Sigma 3 (2015), e24, 63 pp.
Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps
(arXiv:1403.2991 | Published Version)
(with Jonas Azzam, and Tatiana Toro)
[Click to Show/Hide Abstract]
Citation: J. Azzam, M. Badger, T. Toro, Quasiconformal planes with bi-Lipschitz pieces and extensions of almost affine maps, Adv. Math. 275 (2015), 195-259.
Multiscale analysis of 1-rectifiable measures: necessary conditions
(arXiv:1307.0804 | Published Version)
(with Raanan Schul)
[Click to Show/Hide Abstract]
Citation: M. Badger, R. Schul, Multiscale analysis of 1-rectifiable measures: necessary conditions, Math. Ann. 361 (2015), no. 3-4, 1055-1072.
Beurling's criterion and extremal metrics for Fuglede modulus
(arXiv:1207.5277 | Published Version)
[Click to Show/Hide Abstract]
Citation: M. Badger, Beurling's criterion and extremal metrics for Fuglede modulus, Ann. Acad. Sci. Fenn. Math. 38 (2013), 677-689.
Quasisymmetry and rectifiability of quasispheres
(arXiv:1201.1581 | Published Version)
(with James T. Gill, Steffen Rohde, and Tatiana Toro)
[Click to Show/Hide Abstract]
Citation: M. Badger, J.T. Gill, S. Rohde, T. Toro, Quasisymmetry and rectifiability of quasispheres, Trans. Amer. Math. Soc. 366 (2014), no. 3, 1413-1431.
Flat points in zero sets of harmonic polynomials and harmonic measure from two sides
(arXiv:1109.1427 | Published Version)
[Click to Show/Hide Abstract]
Citation: M. Badger, Flat points in zero sets of harmonic polynomials and harmonic measure from two sides, J. London Math. Soc. 87 (2013), no. 1, 111-137.
Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited
(arXiv:1003.4547 | Published Version)
[Click to Show/Hide Abstract]
Citation: M. Badger, Null sets of harmonic measure on NTA domains: Lipschitz approximation revisited, Math. Z. 270 (2012), no. 1-2, 241-262.
Harmonic polynomials and tangent measures of harmonic measure
(arXiv:0910.2591 | Published Version)
[Click to Show/Hide Abstract]
Citation: M. Badger, Harmonic polynomials and tangent measures of harmonic measure, Rev. Mat. Iberoam. 27 (2011), no. 3, 841-870.

Dissertation

PhD Thesis: Harmonic Polynomials and Free Boundary Regularity for Harmonic Measure from Two Sides. Defended on May 5, 2011.

Slides

Selected slides from research talks and colloquiua, in reverse chronological order:

Open Problems about Curves, Sets, and Measures (Version 2)
PCMI Research Program Seminar. July 2018. Updated version of Talk at ORAM 2018.
Open Problems about Curves, Sets, and Measures
8th Ohio River Analysis Meeting, Lexington, March 2018.
Geometry of Radon measures via Hölder parameterizations
Geometric Measure Theory, Warwick, July 2017.
Structure theorems for Radon measures
Analysis on Metric Spaces, Pittsburgh, March 2017.
Singular Points for Two-Phase Free Boundary Problems for Harmonic Measure
SIAM Minisymposium on New Trends in Elliptic PDE, December 2015.
What is Nonsmooth Analysis?
An introductory colloquium (joint presentation with Vasileios Chousionis) for the UConn Special Semester in Nonsmooth Analysis. September 2015.

[Additional Slides]

Miscellaneous

Brownian Motion Demo
HTML 5 simulation of Brownian motion exiting a domain.
Bee Sting Bee
North American history in Ontario County, NY
Matthew Ward <link to>
Fiction and non-fiction by Connecticut writer Matthew Ward.
Date of Freshest Content: June 30, 2019