Matthew Badger | Department of Mathematics | University of Connecticut

Geometry of Sets and Measures

Matthew at Moraine Lake

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

Fall 2016 Office Hours
M By appointment
Tu 2:00pm - 3:15pm
W 1:25pm - 2:15pm
Th By appointment
F By appointment

Office hours are held in
Monteith 326

Mathematics

I am an Assistant Professor of Mathematics at UConn. 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 Fall 2016, the Analysis and Probability Seminar meets Fridays at 1:30pm. This is a research seminar featuring speakers from around the world. Organized by Vasileios Chousionis and Oleksii Mostovyi.

In Fall 2016, we are also ignaurating the Analysis Learning Seminar, meeting on Tuesdays at 4:00pm. This seminar will feature mini-courses by UConn postdocs and hour-long talks by UConn graduate students. All graduate students and advanced math majors who are interested in analysis are welcome to attend!

Recent and Upcoming Events

Geometric Aspects of Harmonic Analysis: AMS Special Session at the Fall Eastern Sectional Meeting in Brunswick, Maine, September 24 and 25, 2016.

Geometric Measure Theory and Its Applications: AMS Special Session at the Spring Eastern Sectional Meeting in Stony Brook, March 19 and 20, 2016.

Special Semester in Nonsmooth Analysis: UConn Department of Mathematics. Fall 2015.

Complex Analysis, Probability and Metric Geometry: AMS Special Session at the Spring Southeastern Sectional Meeting in Knoxville, March 22 and 23, 2014.

Harmonic Analysis, Partial Differential Equations and Geometric Measure Theory: AMS Special Session at the Joint Mathematics Meeting in San Diego, January 10, 2013.

Teaching

[Math Course Schedules: Current Semester]

Fall 2016

Math 2410, Section 11: Elementary Differential Equations

Math 3150, Section 1: Analysis I

Previous Semesters

Research

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 1500382
Analysis Program. Continuing Grant.
NSF DMS 1203497
2012 NSF Mathematical Sciences Postdoctoral Research Fellowship

Publications and Preprints

[Statistics] Newest preprints/papers are listed first.

Multiscale analysis of 1-rectifiable measures II: characterizations
(arXiv:1602.03823)
(with Raanan Schul)
[Click to Show/Hide Abstract]
Status: Preprint, Submitted.
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)
(with Max Engelstein and Tatiana Toro)
[Click to Show/Hide Abstract]
Status: Preprint, Submitted.
Rectifiability and elliptic measures on 1-sided NTA domains with Ahflors-David regular boundaries
(arXiv:1507.02039)
(with Murat Akman, José María Martell, and Steve Hofmann)
[Click to Show/Hide Abstract]
Status: Accepted. To appear in Trans. Amer. Math. Soc.
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. Iberoamericana 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:

Rectifiable and Purely Unrectifiable Measures in the Absence of Absolute Continuity
JMM 2016 (Seattle), Special Session on Analysis and Geometry in Nonsmooth Metric Measure Spaces, January 2016.
Singular Points for Two-Phase Free Bounbdary 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.
Quasiconformal Planes and Bi-Lipschitz Parameterizations
Ahlfors-Bers VI, October 2014.
Multiscale Analysis of 1-Rectifiable Measures
AMS Fall 2013 Southeastern Sectional Meeting, Special Session on Harmonic Analysis and PDE, Louisville, October 2013.
Quasispheres and Bi-Lipschitz Parameterizations
Perspectives in Analysis, Philadelphia, September 2012.
Harmonic Measure from Two Sides (and Tools from Geometric Measure Theory)
Simons Postdoctoral Fellowship Meeting, April 2012.
Harmonic Measure in Space (Brownian Motion Demonstrations)
Dynamics seminar at Stony Brook University, September 2011.
Free Boundary Regularity for Harmonic Measure from Two Sides
JMM 2011 (New Orleans), Special Session on Harmonic Analysis and PDEs, January 2011.
Lipschitz Approximation to Corkscrew Domains
Rainwater Seminar at University of Washington, February 2010.
Tangent Measures and Harmonic Polynomials
Short talk at CRM, June 2009.

Miscellaneous

Bee Sting Bee
North American history in Ontario County, NY
Sage <link to>
Open Source Mathematics Software
Date of Freshest Content: August 17, 2016