Curriculum Vitae
Address
Department of Mathematical Sciences
1 University of Arkansas
SCEN 327
Fayetteville, AR 72701
araich@uark.edu
479-575-8630 (fax)
http://comp.uark.edu/~araich/
Current Position
Past Positions
- Visiting Professor, Universidade Federal de São Carlos, Sept. 2018
- Associate Professor, University of Arkansas,
Fall 2013 - Spring 2018
- Visiting Fellow, University of Cambridge, Sept. 2015 - Aug. 2016
- Assistant Professor, University of Arkansas ,
Fall 2008 - Spring 2013
- Visiting Fellow, The Erwin Schrodinger International Institute
for Mathematical Physics, Oct. 2005, Nov. 2006, Nov. 2009, Dec. 2010
- Visiting Assistant Professor, Texas A&M University, Fall 2005 - Spring 2008
- Visiting Fellow, Isaac Newton Institute,
May 11 - May 19, 2007
Education
Research Interests
- Several Complex Variables
- Partial Differential Equations
- Harmonic Analysis
Grants
- Simons Foundation Collaboration Grant ($42,000) 2020 - 2025.
This grant provided travel funds to support my research in several complex variables and partial differential equations.
- NSF Award DMS-1841778 ($22,127) 2018-2019.
Principal Investigator. This grant supported the UFSCar International Workshop on Partial Differential Equations and Complex Analysis in São Carlos, Brazil..
- NSF Award DMS-1405100, ($133,318) 2014 - 2017. Principal Investigator. This was an individual research grant to support my research in Analysis and CR Geometry in Several Complex Variables.
- Simons Foundation Collaboration Grant ($7,000) 2013 - 2014.
This grant provided travel funds to support my research in several complex variables.
- NSF Award DMS-1157517, ($89,999) 2012 - 2015. Co-Principal Investigator. This grant supports the 2012, 2013, and 2014 Spring Lecture Series.
- NSF Award DMS-0963810, ($85,762) 2010 - 2013. Principal Investigator. This grant supported the 2010, 2011, and 2012 Spring Lecture Series.
- NSF Award DMS-0855822, ($95,602) 2009 - 2013. Principal Investigator. This was an individual research grant to support my research in Heat Equations, Boundary Operators and CR Geometry in Complex Analysis.
Awards and Honors
- Plenary Speaker, Spring Western Sectional Meeting of the AMS, Spring 2017
- Fulbright College Master Researcher Award, University of Arkansas, 2016
- Cambridge Faculty Fellowship, University of Arkansas, Fall 2015 - Spring 2016
- "Meritorious Service Award", Department of Mathematical Sciences, University of Arkansas, Spring 2014
- "Excellence in Teaching Award", University of Arkansas, Spring 2012
Selected by the Graduate Assistants in the Department of Mathematical Sciences
- "You've Made a Difference", University of Arkansas, Fall 2011
Identified by a first-year student on the MAP-Works survey through University Housing as having helped the most in his/her college success during the first few weeks of school.
- 2009 Conner Faculty Fellow, Fulbright College of Arts & Sciences,
University of Arkansas, 2009
- Vertical Integration of Research and Education (VIGRE) Fellowship,
University of Wisconsin-Madison Mathematics Department, 2001
- L&S Teaching Fellow, College of Letters and Sciences,
University of Wisconsin-Madison,
Fall 2001 - Spring 2002
One of eighteen chosen from a pool of over 1000 candidates
- Sustained Excellence in Teaching and Service Award,
University of Wisconsin-Madison
Mathematics Department, Spring 2001
- Excellence in Teaching Award, University of Wisconsin-Madison
Mathematics Department, Spring 2000
- "Superior" rating in TA evaluations, University of Wisconsin-Madison
Mathematics Department,
Fall 1998, 1999, 2000, 2002, 2004, Spring 1999, 2000, 2002
- Sigma Xi, Williams College, Nominated spring 1998
- Morgan Prize for Teaching and/or Applied Math, Williams College, Spring 1998
Publications and Preprints
- "Analysis on Quadrics", with Al Boggess, submitted.*
- "Weighted Hardy Space and Ultradistributions", with Gustavo Hoepfner and Patricia Rampazo, submitted.
- "The Fundamental Solution to $\Box_b$ on Quadric Manifolds with Nonzero Eigenvalues",
with Al Boggess, submitted.
- "Global Gevrey Vectors", with G. Hoepfner and P. Rampazo, submitted.
- "Distributions with Decay and Restriction Problems", with Gustavo Hoepfner, submitted.
- "Boundary invariants and the closed range property for $\bar\partial$", with Phillip Harrington, submitted.
- "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 3. Asymptotics for a
Codimension 2 case in $\mathbb{C}^4$", with Al Boggess, to appear,
J. Geom. Anal..
- "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 1. General Formulas",
with Al Boggess,
to appear, Proc. Amer. Math Soc.
- "Strong Closed Range Estimates: Necessary Conditions and Applications", with Phillip Harrington, to appear, Indiana Univ. Math. J.
- "Compactness of the complex Green operator on
non-pseudoconvex CR manifolds", with Joel Coacalle,
Commun. Pure Appl. Anal., 20(6):2139--2154, 2021.
- "Closed range estimates for $\bar\partial_b$ on CR manifolds of hypersurface type", with Joel Coacalle, J. Geom. Anal., 31(1): 366--394, 2021.
- "$L^p$-Estimates for the $\bar\partial_b$-equation on a class of infinite type domains", with Khanh Tran, Math. Nachr., 294(1):82--97, 2021.
- "The complex Green operator with Sobolev estimates up to a finite order," with Bingyuan Liu,
Internat. J. Math., 31(14), 2050122, 19pp, 2020.
- "The Kohn-Laplace equation on abstract CR manifolds: Global regularity", with Khanh Tran,
Trans. Amer. Math. Soc., 373(11): 7575--7606, 2020.
- "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 2. $L^p$ Regularity and Invariant Normal Forms", with Al Boggess,
Complex Anal. Synerg., 6(2): Paper No. 13, 19pp, 2020.
- "Closed range of $\bar\partial$ on unbounded domains in $\mathbb{C}^n$",
with Phillip Harrington, J. Anal. Math., 138(1):185--208, 2019.
- "Global $L^q$ Gevrey Functions, Paley-Weiner Theorems, and the FBI Transform", with Gustavo Hoepfner,
Indiana Univ. Math. J, 68(3): 967--1002, 2019.
- "Microglobal Regularity and the Global Wavefront Set",
with Gustavo Hoepfner, Math. Z. 291(3-4): 971--988, 2019.
- "The Bergman Kernel on Forms: General Theory,
Proc. Amer. Math Soc., 146(11): 4683--4692, 2018.
- "Closed range of $\bar\partial$ in $L^2$-Sobolev spaces on unbounded domains in $\mathbb C^n$", with Phillip Harrington,
J. Math. Anal. Appl459(2): 1040--1061, 2018.
- "Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior", with Minh Kha and Peter Kuchment,
Journal of Spectral Theory, 7(4): 1171--1233, 2017
- "WHAT IS a CR Manifold?", with Phillip Harrington,
Notices Amer. Math. Soc., 64(7): 722-724, 2017.
- "Global $L^q$-Gevrey functions and their applications", with Ziad Adwan and Gustavo Hoepfner,
J. Geom. Anal., 27(3): 1874-1913, 2017.
- "A remark on boundary estimates on unbounded $Z(q)$ domains in $\mathbb C^n$", with Phillip Harrington,
Complex Var. Elliptic Equ., 62(9): 1192-1203, 2017. (arXiv:1512.02523)
- "Schr\"odinger Operators With $A_\infty$ Potentials", with Michael Tinker,
Potential Analysis, 45(2): 387-402, 2016.
-
"Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds", with Phillip Harrington,
Ann. Inst. Fourier (Grenoble)
, 65(4): 1711-1754, 2015. (arXiv:1408.4182)
- "The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension", with Michael Tinker,
Complex Var. Elliptic Equ., 60(10): 1366-1373, 2015. (ariXiv:1408.4182)
- "Taylor Series of Conformal Mappings onto Symmetric Quadrilaterals", with Loredana Lanzani and Jeanine Myers,
Complex Var. Elliptic Equ., 60(8): 1133-1141, 2015.
- "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt,
Complex Var. Elliptic Equ., 60(4): 478-492, 2015.
(arXiv:1208.2192)
-
"Regularity equivalence of the Szeg\"o projection and the complex Green operator",
with Phillip Harrington and Marco Peloso, Proc. Amer. Math. Soc., 143(1): 353-367, 2015.
- "$L^p$-Estimates for the $\bar\partial$-equation on a class of infinite type domains",
with Ly Kim Ha and Khanh Tran,
Internat. J. Math., 25(11): 2014. 1450106 (15 pages).
- "Sobolev spaces and elliptic theory on unbounded domains in $\mathbb R^n$", with Phillip Harrington,
Adv. Differential Equations, 19(7/8): 635-692, 2014.
(arXiv:1209.4044)
- "Div-curl type inequalities for higher order operators", with Loredana Lanzani,
Advances in Analysis: The Legacy of Elias M. Stein (Princeton Mathematical Series). Princeton U. Press, (2013).
ISBN: 9780691159416.
- "Defining functions for unbounded $C^m$ domains", with Phillip Harrington,
Rev. Mat. Iberoam. 29(4):1405-1420, 2013.
- "Fundamental solutions to $\Box_b$ on certain quadrics", with Albert Boggess,
J. Geom. Analysis 23(4):1729-1752, 2013. (arXiv:1110.5804)
-
"Heat kernels, smoothness estimates and exponential decay", with
Albert Boggess, J. Fourier Anal. Appl., 19:180-224, 2013.
- "Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case.",
with Peter Kuchment, Math. Nachr, 285:1880-1894, 2012.
-
"An Aronsson type approach to extremal quasiconformal mappings", with Luca Capogna,
J. Differential Equations, 253:851-877, 2012.
- "Heat equations and the weighted $\bar\partial$-problem",
Commun. Pure Appl. Anal., 11(3):885-909, 2012.
- "The $\Box_b$-heat equation on quadric manifolds", with Albert Boggess,
J. Geom. Analysis, 21:256-275, 2011.
- "Regularity results for $\bar\partial_b$ on CR-manifolds of hypersurface type",
with Phillip Harrington,
Comm. Partial Differential Equations.
36:134-161, 2011.(arXiv:0912.2823)
- "Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type",
Math. Ann., 348: 81-117, 2010. (arXiv:0810.2553)
-
"A Simplified Calculation for the Fundamental Solution to the Heat Equation on the Heisenberg
Group", with Albert Boggess, Proc. Amer. Math. Soc.,
137:937-944, 2009.
- "Compactness of the Complex Green Operator", with Emil J. Straube,
Math. Res. Lett.
15: 761--778, 2008.
-
"Pointwise Estimates for Relative Fundamental Solutions of Heat Equations
in $\mathbb{R}\times\mathbb{C}$",
Math. Z., 256: 193-220, 2007.
- "Heat Equation in $\mathbb{R}\times\mathbb{C}$",
J. Funct. Anal.,
240: 1-35, 2006.
- "One-Parameter Families of Operators in $\mathbb{C}$",
J. Geom. Analysis,
16(2):353-374, 2006.
- "Infinite ergodic index $\mathbb{Z}^d-actions in infinite measure$", with E. J. Muehlegger,
C. E. Silva,
M. P. Touloumtzis, B. Narasimhan and W. Zhao.
Colloq. Math,
82:167-190, 1999.
- "Lightly mixing on dense algebras", with E. J. Muehlegger,
C. E. Silva
and W. Zhao. Real Analysis Exchange. 23:259-265, 1997/98.
* -- denotes an expository article.
Teaching Experience
- Introduction to Partial Differential Equations, University of Arkansas
- Elementary Analysis, University of Arkansas
- Complex Variables I and II, University of Arkansas
- Advanced Calculus I and II, University of Arkansas
- Functional Analysis, University of Arkansas
- Partial Differential Equations, University of Arkansas
- Ordinary Differential Equations, University of Arkansas
- Calculus I and II, University of Arkansas
- Differential Equations, Texas A&M University
- Engineering Mathematics III, Texas A&M University
- Engineering Mathematics II, Texas A&M University,
- Business Mathematics II, Texas A&M University,
- Business Mathematics I, Texas A&M University,
- Calculus & Analytic Geometry, University of Wisconsin-Madison,
- Arithmetical Problem Solving, University of Wisconsin-Madison,
Professional Experience
Service and Committee Work
- Graduate Coordinator: Dept. Math. Sci., U. Arkansas, Fall 2021- current.
- Co-organizer: Virtual East West Several Complex Variables
Seminar, Fall 2020-current.
- Chair: Hiring Search Committee, Dept. Math. Sci., U. Arkansas, Fall 2021-Spring 2022.
- Member: Promotion and Tenure Committee, Dept. Math. Sci., U. Arkansas, Fall 2021-current.
- Calculus Success Rates Working Group: U. Arkansas, Fall 2019-current.
This is a working group with Engineering, Pearson, Math, and the Student Success Folks to look at historical Pearson usage data among
Calculus I and II students to build an early warning system to detect students at risk of a grade of D, W, or F. We debuted the system during the Fall 2020 semester and expanded to cover College Algebra, Finite Math, and Business Calculus in Spring 2021.
- Undergraduate Coordinator: Dept. Math. Sci., U. Arkansas, Fall 2017-Spring 2021.
- DEI Committee Co-chair: Dept. Math. Sci., U. Arkansas Fall 2019-Spring 2020.
DEI stands for Diversity, Equity, and Inclusion, and the function of the committee is generate policy and actions for the Department of Mathematical Sciences to increase the representation and inclusion for Underrepresented Groups.
- Co-organizer: UFSCar International Workshop on Partial Differential Equations and Complex Analysis in São Carlos, Brazil. August 2018.
This is a official Satellite Conference of the International Congress of Mathematicians 2018 in Sao Paolo, Brazil.
- Co-organizer: Special Session on Several Complex Variables and PDEs at the
Spring 2017 Western Sectional Meeting of the AMS,
Washington State University. April 2017.
- Instructor: Osher Lifelong Learning Institute, March 2017
OLLI sponsored courses provide high quality, affordable educational, cultural, and engagement opportunities for seasoned adults. I taught a four hour class over two weeks about cardinality and the Cantor set.
- Curriculum Committee Chair: Dept. Math. Sci., U. Arkansas, Fall 2014-Spring 2015, Fall 2016-Spring 2017.
- Hiring Committee: Dept. Math. Sci., U. Arkansas, Fall 2016-Spring 2017.
- Third Year Review Committee: Dept. Math. Sci., U. Arkansas, Fall 2016-Spring 2017.
- Faculty Mentor: Dept. Math. Sci., U. Arkansas, Fall 2014-current
- Contact Organizer, Harmonic Analysis, d-bar, and CR Geometry (15w5074), BIRS-CMO, Oaxaca, Mexico, Oct. 2015.
- Chair, Mathematical Sciences Steering Committee, Fall 2015 - Spring 2016
- Mathematical Sciences Steering Committee, Fall 2013 - Spring 2015
- Organizer, University of Arkansas Spring Lecture Series in the Mathematical Sciences: 2010, 2011, 2014
- Co-organizer, Celebration of the Mind, 2012, 2013.
Faculty Mentor, 2014 - current.
I am a co-organizer of a Math Fair for high school students and the community at large.
The Celebration of Mind is a math fair for K-12 students andand the community at large.
We enlisted graduate and undergraduate math students design interactive math games and projects for the fair.
We tie the projects directly to the Common Core Standards for Mathematics and provide handouts for the teachers that detail the activities and their tie-in to the standards.
Our goal is to increase the number of math and statistics majors at the University of Arkansas and anticipate that the fair will happen annually.
- Instructor, M-SEA program, Summers 2011 - 2013
My colleague Janet Woodland and I organized a session for the
Mathematics, Science and Engineering Academy (M-SEA) run by the Cooperative Developmental Energy Program (CDEP) at Fort Valley State University. CDEP is a program whose
goal is to increase the number of women and minorities in the geosciences. Fort Valley offers a 3-2 program -- earn a B.S. at Fort Valley in three years and a second B.S. at a partner institution
in two years. The University of Arkansas is one of the partner institutions. The M-SEA is a program that identifies and prepares talented girls and minorities to enter CDEP.
The students enroll in eighth grade and their summers are spent at Fort Valley and the partner institutions receiving education and training. Dr. Woodland and I developed a class in which we had the students
derive a discrete version of Fick's Law of Diffusion and model lake pollution. We then pointed out that the mathematical underpinnings of Fick's Law of Diffusion are the same as Newton's Law
of Cooling, Fourier's Law of Heat Conduction, and Ohm's Law of Electrical Conduction.
- Project Reviewer:
- Universita degli Studi di Milano -- I served as a referee to comment on a project under review for research financing
- Universita degli Studi di Padova -- I served as an external reviewer on a Ph.D. candidate's research achievements and also wrote a letter of recommendation for a post-doc applying for
an internal research award
- Mathematical Sciences Graduate Committee, Fall 2010 - Spring 2013
- Mathematical Sciences Library Representative, Fall 2009 - Spring 2013
- Reviewer: Mathematical Reviews: (for the American Mathematical Society), Fall 2008 - current
- Mathematical Sciences Hiring Committee, Fall 2008
- Volunteer Instructor, Summer Educational Enrichment
in Math, June 2006, July 2007
Planned and led three 2.5 hour workshops titled "How Google Works" for incoming 6th, 7th, and 8th graders
- Organizer, Several Complex Variables Seminar, Texas A&M University, June 2006 - May 2008
- Volunteer, Texas Science Olympiad,
April 2006
- Volunteer Speaker, East High School Math Week, Madison, WI, May 2005
Invited Talks (International)
- "The $\Box_b$-equation on quadric submanifolds",
Virtual East-West Several Complex Variables seminar, May 2020.
- "Distributions with Decay and Restriction Problems"
- ``Introduction to CR Geometry and the Tangential Cauchy-Riemann Operator", A Minicourse at the
10th Workshop on Geometric Analysis of PDEs and Several Complex Variables,
Serra Negra, Brazil, Aug. 2019.
- Lecture 1: An Introduction to CR Geometry
- Lecture 2: The tangential Cauchy-Riemann operator and the Levi form
- Lecture 3: The $\bar\partial_b$-problem on the Heisenberg group
- Lecture 4: CR Geometry and d-bar today: The $\Box_b$-problem on Quadric Submanifolds of $\mathbb{C}^n\times\mathbb{C}^m$.
- "The complex Green operator on quadric submanifolds", II Joint Meeting of the Spanish and Brazilian Mathematics Societies,
Special Session in Complex Analysis and Operator Theory, Cadiz, Spain, Dec. 2018.
- "The Global Behavior of the Fourier and FBI Transforms",
Partial Differential Equations Seminar, University of Wollongong, Australia, Oct. 2018.
- "Global $L^q$ Gevrey Functions and Applications", Symposium in Harmonic Analysis and Geometric Measure Theory,
University of São Paulo, Ribeirão Preto, Brazil, August 2018.
- "Boundary invariants and the closed range property for $\bar\partial$", UFSCar International Workshop on Partial Differential
Equations and Complex Analysis",/a>, Universidade Federal de São Carlos, Brazil, Aug. 2018.
- "CR Invariants and Solvability of the $\bar\partial$-equation", CR-Geometry and PDEs VIII, Levico Terme, Italy, June 2018.
- "The Global Behavior of the Fourier and FBI transforms",
- "The complex Green operator on quadric submanifolds in $\mathbb{C}^4$", Workshop on d-bar at NTNU Trondheim, Norway, Trondheim, Norway, Oct. 2017.
- "The complex Green operator on quadric submanifolds", Analysis and geometry in several complex variables II, Doha, Qatar, Jan. 2017
- "The $L^2$-theory of the d-bar equation on unbounded domains", Mathematics Colloquium, Fudan University, Shanghai, June 2016.
- "Global $L^q$-Gevrey Functions Spaces with Applications", Workshop on
Harmonic Analysis and Several Complex Variables, Vietnam Institute for the Advances Study in Mathematics, Hanoi, Vietnam,
June 2016.
- "Complex Analysis -- Simplified!", Wolfson College Science Society Seminar, University of Cambridge, Cambridge, UK, Apr.~2016.
- "Global $L^q$-Gevrey Function Spaces",
- Mathematics Colloquium, Universidade Federal de S\~ao Carlos, Mar. 2016
- Several complex variables and CR geometry,
International Erwin Schrodinger Institute for Mathematical Physics, Nov. 2015.
- "The dbar-equation on unbounded domains",
- Geometric Analysis and Partial Differential Equations Seminar, University of Cambridge, Cambridge, England, Oct. 2015.
- BIRS-CMO, Oaxaca, Mexico, Oct. 2015.
- "The Box_b-heat equation on quadric submanifolds", Analysis Seminar, Universit\`a degli Studi di Milano, Milan, Italy, June 2015.
- "Regularity of the Bergman Projection", Analysis and Geometry in Several Complex Variables, Doha, Qatar, Janunary 2015.
- "The $\Box_b$-heat equation for the Heisenberg group and quadric submanifolds", Analysis Seminar, Universit\`a degli Studi di Milano, Milan, Italy, June 2014.
- "$L^p$-Sobolev and H\"older Estimates for the Bergman kernel", Analysis Seminar, Universit\`a degli Studi di Padova, Padua, Italy, June 2014.
- "Box-b heat kernel decay and the Fourier transform", Analysis Seminar, University of British Columbia, Vancouver, Canada, November 2012.
- "Closed range for d-bar on (0,q)-forms and a weak Z(q)-condition", Workshop: CR-Geometry and PDEs - V, Levico Terme, Trento, Italy, June 5-8, 2012.
- "Gaussian estimates for $\Box_b$-heat kernels and quantitative smoothness estimates",
The dbar-Neumann Problem: Analysis, Geometry and Potential Theory,
International Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria, Dec. 2010.
- "Heat kernel decay via the Fourier transform",
Spectral Theory of Operators in Analytic Functions Spaces. Centre
International de Recontres Mathemathique, Marseilles, France, April 2010
- "Closed range of dbar-b on CR manifolds of hypersurface type",
The dbar-Neumann Problem: Analysis, Geometry and Potential Theory,
International Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria, Nov. 2009.
- "Compactness of the Complex Green Operator on CR Manifolds of Hypersurface Type",
First Joint International Meeting of the AMS with CMS, Special Session on Several Complex Variables and Applications,
Shanghai, China, Dec. 2008
-
"Pointwise heat kernel estimates with applications to complex analysis".
Complex Analysis, Operator Theory, and Applications to Mathematical Physics -- Followup Fall 2006,
International Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria, Nov. 15, 2006.
-
"Pointwise Estimates for Relative Fundamental Solutions of Heat Equations
in $\R\times\C$." International Conference in PDE, Complex Analysis, and Differential Geometry,
Notre Dame University, June 13, 2006.
- "Estimates of heat kernels for the $\Box_{\tau p}$ heat equation in $\mathbb{R}\times\mathbb{C}$"
Program in Complex Analysis, Operator Theory, and Applications to Mathematical Physics:
Workshop: Complex Analysis and Partial Differential Equations,
International Erwin Schrodinger Institute for Mathematical Physics, Vienna, Austria, Oct. 27, 2005
Invited Talks (Domestic)
- "Compactness of the complex Green operator on non-pseudoconvex CR manifolds",
Joint Mathematics Meeting 2022,
AMS Special Session on Partial Differential Equations and Complex Variables, Seattle, WA, Jan. 2022.
- "The $\Box_b$-equation on quadric submanifolds and applications",
Joint Mathematics Meeting 2022,
AMS Special Session on Several Complex Variables Geometric PDE and CR Geometry, Seattle, WA, Jan. 2022.
- "Distributions with Decay and Restriction Problems", AMS 2019 Fall Central Sectional Meeting #1150,
Special Session on Recent Developments in Harmonic Analysis, Madison, WI, Sep. 2019.
- "Strong Closed Range Estimates: Necessary Conditions and Applications", AMS 2019 Fall Central Sectional Meeting #1150,
Special Session on Several Complex Variables, Madison, WI, Sep. 2019.
- "Boundary invariants and the closed range property for $\bar\partial$",
- "Boundary invariants and the closed range property for d-bar", AMS 2018 Spring Central Sectional Meeting #1136,
Special Session on Several Complex Variables, Columbus, OH, Mar. 2018.
- "The Global Behavior of the Fourier and FBI transforms", Analysis Seminar, UC-Irvine, Jan. 2018.
- The Bergman kernel on forms: General theory
- "The Box_b-heat equation on quadric submanifolds,"
- "The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension",
AMS 2015 Spring Central Sectional Meeting #1108,
Special Session on Complex Analysis in Several Variables and its Applications,
East Lansing, MI, March 2015.
- "Closed range of d-bar and a weak Z(q) condition", Complex and Harmonic Analysis Lectures in Honor of Alex Nagel,
Madison, WI, Apr. 2013
- "The Kerzman-Stein operator for piecewise continuously differentiable regions", AMS 2012 Fall Central Sectional Meeting #1084, Special Session on Complex Analysis and
its Broader Impacts, Akron, OH Oct. 2012.
- "Defining functions on unbounded domains in $\mathbb R^n$"
AMS 2012 Spring Central Section Meeting #1081, Special Session on Interplay between Geometry and Partial Differential Equations in Several Complex Variables,
Lexington, KY, Mar. 2012.
- "Part 1: The Mathematics and Statistics Graduate Program at the
University of Arkansas. Part 2: Convergence of Power Series -- Think You're An Expert? Think
Again!", Colloquium, University of Arkansas-Fort Smith, Nov. 2011.
- "An Aronsson type approach to extremal quasiconformal mappings", AMS 2011 Fall Eastern Sectional Meeting #1072, Special Session on Geometric Aspects of Analysis and Measure Theory,
Ithaca, NY, Sep. 2011.
- "Heat kernels, Gaussian decay and the Fourier transform'', Several Complex Variables Seminar, Texas A&M University, Feb. 2011.
- "How to study for graduate math classes and conduct research in mathematics",
Graduate Student Seminar, University of Arkansas, August 2010.
- "Applying for academic jobs in the mathematical sciences", Graduate Student Seminar, University of Arkansas, March 2010.
- "The Box_b-heat kernel on quadric manifolds", Mathematics Colloquium, Georgetown University, Oct. 2009.
- "Compactness of the complex Green operator", Mathematics Colloquium, Notre Dame University, April 2009
- "Compactness of the complex Green operator on CR manifolds of hypersurface type",
AMS Spring Central Sectional Meeting #1047 ,
Special Session on Holomorphic and CR Mappings,
Urbana, IL, Mar. 2009.
- "The weighted $\bar\partial$-heat equation with applications", Analysis and PDE Seminar,
Johns Hopkins University, Nov. 2008.
- "On A Class of Integral Operators Related to the Weighted $\bar\partial$-equation in $C$",
AMS Southeastern Sectional Meeting #1037,
Special Session on Harmonic Analysis and Partial Differential Equations in Real and Complex Domains, Baton Rouge, LA,
Mar. 2008.
-
"Compactness of the complex Green operator II",
AMS Eastern Sectional Meeting #1031,
Special Session on Geometric Analysis of Complex Laplacians,
New Brunswick, NJ, Oct. 2007.
- "Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, III",
Several Complex Variables Seminar, Texas A&M University, May 4, 2007.
- "Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, II",
Several Complex Variables Seminar, Texas A&M University, Apr. 27, 2007.
- "Techniques for Pointwise Estimates for a Class of Heat Kernels in RxC, I",
Several Complex Variables Seminar, Texas A&M University, Apr. 20, 2007.
- "Heat Kernel Estimates with Applications to Complex Analysis."
2007 AMS Spring Central Section Meeting #1025,
Special Session on PDE Methods in Several Complex Variables,
Oxford, OH, Mar. 17, 2007.
- "Pointwise Estimates for Heat Kernels in
$\mathbb{R}\times\mathbb{C}\times\mathbb{C}$."
AMS Southeastern Sectional Meeting #1022,
S3A - Special Session on Boundary Operators in Real and Complex Domains,
University of Arkansas-Fayetteville, Nov. 2006.
- "An introduction to the spectral theorem with an application to PDEs",
VIGRE Seminar,
University of Georgia, May 2, 2006.
- "Pointwise estimates on kernels of a family of heat
equations in $\mathbb R\times \mathbb C$ with applications to several
complex variables"
- "Scaling and PDEs -- how to solve a differential equation without doing any work", Pi Mu Epsilon
Undergraduate Math Club Talk, Texas A&M University, April 24, 2006.
- "A gentle introduction to $\bar\partial_b$ on the Heisenberg group", a series of four seminar
talks in the Several Complex Variables Seminar,
Texas A&M University, Spring 2006.
- "Estimates of heat kernels for the $\Box_{\tau p}$ heat equation in $\mathbb{R}\times\mathbb{C}$"
Several Complex Variables Seminar,
Texas A&M University, Oct. 14, 2005
- "The magic of conditional convergence." Math Week, Madison East High School, May 2005.
- "Heat equations in $\mathbb{R}\times\mathbb{C}$"
-
"Heat equations and the $\bar\partial$-problem on weighted $L^2$ spaces
in $\mathbb{C}$". Special Session: Complex and Functional Analysis II, Joint
Mathematical Meetings, Atlanta, Georgia, Jan. 8, 2005
- "Heat kernels and the weighted $\bar\partial$-equation on $\mathbb{C}$"
- "On the $\bar\partial$-equation in $L^2(\mathbb{C},e^{-2\varphi})$."
Specialty exam, University of Wisconsin-Madison, Jan. 2002
- "On limits of sequences of operators: a theorem of Stein". A series of three lectures
at the Graduate Student Analysis Seminar, University of Wisconsin-Madison, Feb. 2001
- "Mixing drinks and kneading bread: an introduction to ergodic theory". Graduate
Student Analysis Seminar, University of Wisconsin-Madison, Nov. 1999.
- "Lightly mixing on dense algebras".
Hudson River Undergraduate Mathematics Conference,
Williams College, Apr. 1997.