# Anne-Katrin Gallagher (née Herbig)

### Academic Positions

2016-2018: tenure-track Assistant Professor, Department of Mathematics, Oklahoma State University, Stillwater, OK

2015-2016: Post Doc, Department of Mathematics, University of Greifswald, Greifswald, Germany

2013-2015: Designated Associate Professor, Graduate School of Mathematics, Nagoya University, Nagoya, Japan

2011-2013: Senior Post Doc, Principal Investigator, Department of Mathematics, University of Vienna, Vienna, Austria; funded by the Austrian Science Fund

2007-2011: Post Doc, Department of Mathematics, University of Vienna, Vienna, Austria; funded by the Austrian Science Fund

2004-2007: Assistant Professor Post Doc, Department of Mathematics, University of Michigan, Ann Arbor

1999-2004: Graduate Teaching Associate, Department of Mathematics, The Ohio State University, Columbus, OH

### Education

2013: Habilitation, Mathematics, University of Vienna, Vienna, Austria

2004: Ph.D., Mathematics, The Ohio State University, Columbus, OH

2000: M.S., Mathematics, The Ohio State University, Columbus, OH

### Publications

Published papers and preprints

A.-K. Gallagher, Equivalence between validity of p-Poincaré inequality and finiteness of the strict p-capacitory inradius, preprint (2024, 15 pgs.)

A.-K. Gallagher, On the Poincaré inequality on open sets in R^n, appears online in Computational Methods and Function Theory, preprint (2023, 21 pgs.)

A.-K. Gallagher, P. Gupta, L. Vivas, On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces, to appear in Indiana Univ. Math. J., preprint (2022, 9 pgs.)

A.-K. Gallagher, T. Harz, On plurisubharmonic defining functions for pseudoconvex domains in C^2, preprint (2022, 32 pgs.)

A.-K. Gallagher, P. Gupta, L. Vivas, On the dimension of Bergman spaces on P^1, Mathematica 1, No. 3, 666-684 (2022, 19 pgs.), preprint

A.-K. Gallagher, P. Gupta, L. Lanzani, L. Vivas, Hardy spaces for a class of singular domains, Math. Z. 299 (2021), no. 3-4, 2171-2197, preprint

A.-K. Gallagher, J. Lebl, K. Ramachandran, The closed range property for the dbar-operator on planar domains, J. Geom. Anal., 31 (2021), 1646-1670, preprint

A.-K. Gallagher, J. Lebl, K. Ramachandran, Convexity of level lines of Martin functions and applications, Anal. Math. Phys. 9 (2019), no. 1, 443-452, preprint

A.-K. Gallagher, T. Harz, G. Herbort, On the dimension of the Bergman space for some unbounded domains, J. Geom. Anal. 27 (2017), no. 2, 1435-1444, preprint

A.-K. Herbig, J. D. McNeal, On closed range for dbar, Complex Var. Elliptic Equ. 61 (2016), no. 8, 1073-1089, preprint

A.-K. Herbig, J. D. McNeal, E. J. Straube, Duality of spaces of holomorphic functions and smoothing properties of the Bergman projection, Trans. Amer. Math. Soc. 366 (2014), no. 2, 647-665, preprint

A.-K. Herbig, A note on a smoothing property of the harmonic Bergman projection, Internat. J. Math. 24 (2013), no. 4, 1350032, 14 pp., preprint

A.-K. Herbig, J. D. McNeal, Oka's lemma, convexity, and intermediate positivity conditions, Illinois J. Math. 56 (2012), no. 1, 196-211, preprint

A.-K. Herbig, J. D. McNeal, A smoothing property of the Bergman projection, Math. Ann. 354 (2012), no. 2, 427-449, preprint

A.-K. Herbig, J. D. McNeal, Convex defining functions for convex domains, J. Geom. Anal. 22 (2012), no. 2, 433-434, preprint

P. Duren, A.-K. Herbig, D. Khavinson, Robert Jentzsch - Mathematiker und Poet, Mitteilungen der DMV 16 (2008), no. 4, 233-240

J. E. Fornæss, A.-K. Herbig, A note on plurisubharmonic defining functions in C^n, Math. Ann. 342 (2008), no. 4, 749-772, preprint

P. Duren, A.-K. Herbig, D. Khavinson, Robert Jentzsch, mathematician and poet, Math. Intelligencer 30 (2008), no. 3, 18-24

J. E. Fornæss, A.-K. Herbig, A note on plurisubharmonic defining functions in C^2, Math. Z. 257 (2007), no. 4, 769-781, preprint

A.-K. Herbig, A sufficient condition for subellipticity of the dbar-Neumann operator, J. Funct. Anal. 242 (2007), no. 2, 337-362, preprint

A.-K. Herbig, J. D. McNeal, Regularity of the Bergman projection on forms and plurisubharmonicity conditions, Math. Ann. 336 (2006), no. 2, 335-359, preprint

In preparation

A.-K. Gallagher, A note on the Diederich-Fornaess and Steinness indices for a class of pseudoconvex domains in C^n

Qualifying theses

A.-K. Herbig, A sufficient condition for subellipticity of the dbar-Neumann problem on bounded, pseudoconvex domains, Ph.D. thesis (2004), The Ohio State University, Columbus, OH

A.-K. Herbig, The twisted dbar-complex - applications and ramifications, Habilitationsschrift (2013), University of Vienna, Vienna, Austria

### Fellowships and Awards

2023: Ranking (Listenplatz) 3 for W3 Professorship in Complex Analysis at Bergische Universität Wuppertal, Germany

2023: Research in Teams at Banff International Research Station, with P. Gupta and L. Vivas

2022: Summer Research in Mathematics (SRiM) at the MSRI, with P. Gupta and L. Vivas

2020: RiP programme at the Mathematisches Forschungsinstitut Oberwolfach, with P. Gupta, L. Lanzani, and L. Vivas (Covid-related cancelation)

2016&2017: Dean's Incentive Grant, College of Arts and Science, Oklahoma State University

2014-2015: Grant-in-Aid for Young Scientist, funded by the Japanese Society for Promoting Sciences

2011-2014: Elise Richter Scholarship, funded by the Austrian Science Fund

2005: Junior Research Fellow, The Erwin Schrödinger Institute for Mathematical Physics, Vienna, Austria

2005: Rackham Fellowship for Research, University of Michigan

2003&2004: Special Graduate Associate Fellowship, The Ohio State University

2001: Graduate Teaching Associate Award for Excellence in Teaching, Department of Mathematics, The Ohio State University

1998-1999: Fulbright Fellowship, Graduate Student Fellow at The Ohio State University

### Talks

Upcoming Talks

Conference "Midwest Several Complex Variables", Texas A&M, 5/16-5/18/2025

(coorganizer) AMS Sectional Meeting "Several Complex Variables, Partial Differential Equations and CR Geometry" at the JMM 2025, Seattle, 01/08/2025

Conference "Geometric Methods of Complex Analysis", University of Wuppertal, 10/21-10/25/2024

Past Talks

2024

Special Session "Geometric Analysis of SCV and PDEs" at the UMI-AMS Joint Meeting at Università degli Studi di Palermo, 7/25-7/26/2024

Conference "Several Complex Variables, Complex Geometry and related PDEs" at the Brin Mathematics Research Center at University of Maryland, 5/13-5/17/2024

AMS Special Session on Geometric Analysis in Several Complex Variables at the JMM 2024 in San Francisco, 1/5-1/6/2024

2023

Workshop "Analysis and Geometry in Several Complex Variables", Erwin Schrödinger Institute, Vienna, Nov. '23, Video

AWM Special Session on Celebrating the Mathematical Contributions of the AWM, JMM Boston

AMS Special Session on PDEs and Complex Variables, JMM Boston

2022

Complex Analysis Seminar, University of Vienna (Talk 1, Talk 2)

Midwest Several Complex Variables, A conference in Honor of Mei-Chi Shaw

Seminar on (Hyper)Complex Analysis and Geometry at Politecnico Milano

2021

Complex Analysis Seminar, Department of Mathematics, Texas A&M

2020

Virtual East-West Several Complex Variables Seminar

JMM, AWM Workshop: Women in Several Complex Variables

2019

AMS Sectional Meeting: Several Complex Variables, University of Hawaii

Complex Analysis Seminar, Department of Mathematics, University of Wuppertal

2018

Conference in Complex Geometry and Several Complex Variables, Notre Dame University

2017

Workshop on the dbar-operator, NTNU Trondheim

AWM Symposium at UCLA

2016

Analysis Seminar, Department of Mathematics, Oklahoma State University

Geometry Seminar, University of California at Riverside

2015

Seminar for Analysis and Theoretical Physics, Department of Mathematics, University of Hannover

Complex Analysis Seminar, Department of Mathematics, University of Wuppertal

Analysis Seminar, Department of Mathematics, University of Greifswald

Workshop: Analytical aspects of the dbar-equation, Nagoya University

Analysis Seminar, Colloquium, Oklahoma State University

2014

Workshop: Topics in Geometric Analysis on the Bergman kernel, RIMS, Kyoto University

Young Mathematician Workshop on SCV, Pohang University of Science and Technology

Hayama Symposium on Complex Analysis in Several Variables XVII

Workshop: The Cauchy-Riemann equations in several variables, American Institute of Mathematics

Complex Analysis Symposium, Kyushu University

2013

Several Complex Variables Seminar, Department of Mathematics, Tokyo University

Habilitation Colloquium, Department of Mathematics, University of Vienna

Department of Mathematics, University of Adelaide

2012

National Norwegian SCV meeting, NTNU Trondheim

Analysis Seminar, Department of Mathematics, NTNU Trondheim

Analysis Seminar, Department of Mathematics, University of Illinois, Urbana-Champaign

Several Complex Variables Seminar, Department of Mathematics, University of Michigan

Conference Several Complex Variables, University of Ljubljana

Krakow-Vienna workshop: Pluripotential Theory and Several Complex Variables, University of Vienna

National Norwegian SCV meeting, University of Oslo

2011

Workshop in SCV, University of Amsterdam

Minisymposium of the OeMG-Conference - CSASC, University of Graz

Midwest SCV Conference, Washington University in St. Louis

Complex Analysis Seminar, Department of Mathematics, University of Ljubljana

2010

Analysis Seminar, Department of Mathematics, Humboldt University of Berlin

IWOTA 2010, Technical University Berlin

CR Geometry and PDE's IV, CIRM Trento

Nordan Conference

2009

Workshop: The dbar-Neumann problem, Analysis, Geometry and Potential Theory, Erwin Schroedinger Institute for Mathematical Physics

17. OeMG Congress

Complex Analysis Seminar, Department of Mathematics, University of Helsinki

2008

Summer School: Analytic and Algebraic Geometry, Common Problems - Different Methods, IAS, Park City Mathematics Institute

Spring Program: Complex Analysis of Several Variables, Institute Mittag-Leffler

Seminar in SCV and Complex Dynamics, Department of Mathematics, University of Michigan

RTG Working Seminar in SCV and Complex Dynamics, Department of Mathematics, University of Michigan

2007

Mathematical Colloquium, University of Vienna

Banach Center Conference: Complex Function Theory and Geometry

Calderon-Zygmund Analysis Seminar, University of Chicago

AMS Sectional Meeting, Miami University

2006

AMS Sectional Meeting, University of Arkansas

AMS Sectional Meeting, University of Notre Dame

2005

Several Complex Variables Seminar, Department of Mathematics, University of Vienna,

Workshop: Complex Analysis, Operator Theory, and Mathematical Physics, Erwin Schroedinger Institute for Mathematical Physics

Complex Analysis and Geometry Conference, CIRM Luminy

Several Complex Variables Seminar, Department of Mathematics, Purdue University