Gareth James Speight , MMath PhD

I enjoy mathematical analysis that has a geometric flavour. I am particularly interested in geometric measure theory, real analysis, analysis on metric spaces, metric geometry and subriemannian geometry. You can find more information on my webpage.

From January 2016 I am co-organizer of the UC Analysis and PDE seminar.

Between September 2013 and May 2015 I was a postdoctoral researcher in the ERC project Geometric Measure Theory in non-Euclidean Spaces at the Scuola Normale Superiore di Pisa in Italy. My advisor was Luigi Ambrosio.

I obtained my PhD in June 2013 from the Mathematics Institute at the University of Warwick in the United Kingdom. My supervisor was David Preiss.

PhD: University of Warwick UK, 2013 (Mathematics)

MMath: University of Warwick UK, 2009 (Mathematics)

Geometric measure theory, analysis on metric spaces, subriemannian geometry, metric geometry, real analysis.

09-2013 -05-2015 Postdoctoral Researcher, Scuola Normale Superiore di Pisa, Pisa, Italy

01-2016 Faculty Development Fund, University of Cincinnati Domestic Conference Travel Grant to give an invited talk at the Joint Mathematics Meetings 2016 in Seattle $1257

03-2016 Taft Research Center Domestic Conference Travel Grant to give an invited talk at the AMS 2016 Spring Eastern Sectional Meeting $810

05-2016 -08-2016 Taft Research Center Taft Summer Research Fellowship $8000

04-2016 -05-2016 Taft Research Center Taft Research Support Grant for Collaboration on Differentiability of Lipschitz Functions in Carnot Groups $1413

06-2017 Faculty Development Fund Travel grant for summer research travel in 2017. $1970

07-2017 -06-2019 American Mathematical Society and Simons Foundation AMS Simons Travel Grant $4000 Type:Grant

Grant: #DMS-1700077 Investigators:Michael Goldberg, Leonid Slavin, Gareth Speight 02-01-2017 -01-31-2020 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2017-2019 Role:Co-PI $28,000

05-2018 -08-2018 Taft Research Center International Conference Travel Grant $2700

05-2018 Taft Research Center Research Support Grant for research on Geometry and Differentiability in Carnot Groups $2094

05-2019 -06-2019 University of Trento Visiting Professor at the University of Trento $4200

Grant: #576219 Investigators:Gareth Speight 09-2018 -08-2023 Simons Foundation Simons Collaboration Grant: Geometry of Lipschitz Maps and Carnot Groups Role:PI $42,000

05-2019 -08-2019 Taft Research Center Taft Summer Research Fellowship $8000

Grant: #NSF 1856471 Investigators:Speight, Gareth 09-01-2019 -08-31-2020 National Science Foundation Latest in Geometric Analysis Role:PI $44,603 Type:Grant

Grant: #NSF DMS-2000250 Investigators:Michael Goldberg, Leonid Slavin, Gareth Speight 02-2020 -01-2022 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020–2022 Role:Co-PI $16,000 Type:Grant

Grant: #576219 Investigators:Speight, Gareth 09-01-2018 -08-31-2023 Simons Foundation Geometry of Lipschitz Maps and Carnot Groups (Speight) Role:PI $8,400.00 Active Level:Private Non-Profit

Grant: #DMS-2000161 Investigators:Goldberg, Michael; Slavin, Leonid; Speight, Gareth 02-01-2020 -01-31-2023 National Science Foundation Collaborative Research: Ohio River Analysis Meetings 2020-2022 Role:Collaborator $16,000.00 Awarded Level:Federal

Grant: #DMS-2348715 Investigators:Speight, Gareth 09-01-2024 -08-31-2027 National Science Foundation Differentiability in Carnot Groups and Metric Measure Spaces Role:PI 263078.00 Active Level:Federal

Peer Reviewed Publications

D. Bate and G. Speight (2013. ) Differentiability, Porosity and Doubling in Metric Measure Spaces .Proceedings of the American Mathematical Society, , 141 ,971-985

journal paper

G. Speight (2016. ) Lusin Approximation and Horizontal Curves in Carnot Groups .Revista Matematica Iberoamericana, , 32 (4 ) ,1425-1446

journal paper

G. Speight (2013. ) Surfaces Meeting Porous Sets in Positive Measure .Israel Journal of Mathematics, , 196 (1 ) ,435-460

journal paper

G. Speight (2013. ) Directional Lower Porosity .Real Analysis Exchange , , 39 (1 ) ,45-56

journal paper

D. Preiss and G. Speight (2015. ) Differentiability of Lipschitz Functions in Lebesgue Null Sets . Inventiones Mathematicae, , 199 (2 ) ,517-559

journal paper

S. Di Marino and G. Speight (2015. ) The p-Weak Gradient Depends on p .Proceedings of the American Mathematical Society, , 143 ,5239-5252

journal paper

L. Ambrosio and A. Pinamonti and G. Speight (2019. ) Weighted Sobolev Spaces on Metric Measure Spaces .Journal fur die reine und angewandte Mathematik (Crelle's Journal), , 746 ,39-65

journal paper

L. Ambrosio and A. Pinamonti and G. Speight (2015. ) Tensorization of Cheeger Energies, the Space H^{1,1} and the Area Formula for Graphs .Advances in Mathematics, , 281 ,1145-1177

journal paper

A. Pinamonti and G. Speight (2017. ) A Measure Zero Universal Differentiability Set in the Heisenberg Group .Mathematische Annalen, , 368 (1 ) ,233--278

journal paper

E. Le Donne and G. Speight (2016. ) Lusin Approximation for Horizontal Curves in Step 2 Carnot Groups .Calculus of Variations and Partial Differential Equations, , 55 (5 ) ,1--22

journal paper

A. Pinamonti and G. Speight (2017. ) Porosity, Differentiability and Pansu's Theorem .Journal of Geometric Analysis, , 27 (3 ) ,2055–2080

journal paper

A. Pinamonti and G. Speight (2017. ) Structure of Porous Sets in Carnot Groups .Illinois Journal of Mathematics, , 61 (1-2 ) ,127-150

journal paper

A. Pinamonti and G. Speight (2017. ) Expository Article describing A Measure Zero Universal Differentiability Set in the Heisenberg Group .Bruno Pini Mathematical Analysis Seminar, , Feb. 2017 ,85-96

seminar paper

E. Le Donne, A. Pinamonti and G. Speight (2019. ) Universal Differentiability Sets and Maximal Directional Derivatives in Carnot Groups .Journal de Mathematiques Pures et Appliquees, , 121 ,83-112

journal paper

V. Magnani, A. Pinamonti and G. Speight (2020. ) Porosity and Differentiability of Lipschitz Maps from Stratified Groups to Banach Homogeneous Groups .Annali di Matematica Pura ed Applicata, , 199 ,1197-1220

journal paper

P. Lahti, L. Maly, N. Shanmugalingam and G. Speight (2019. ) Domains in Metric Measure Spaces with Boundary of Positive Mean Curvature, and the Dirichlet Problem for Functions of Least Gradient .Journal of Geometric Analysis, , 29 (4 ) ,3176–3220

journal paper

A. Pinamonti and G. Speight (2020. ) Universal Differentiability Sets in Carnot Groups of Arbitrarily High Step .Israel Journal of Mathematics, , 240 ,445-502

preprint

A. Pinamonti, G. Speight, S. Zimmerman (2019. ) A C^m Whitney Extension Theorem for Horizontal Curves in the Heisenberg Group .Transactions of the American Mathematical Society, , 371 (12 ) ,8971-8992

journal paper

M. Capolli, A. Pinamonti and G. Speight A C^m Lusin Approximation Theorem for Horizontal Curves in the Heisenberg Group .Calculus of Variations and Partial Differential Equations, ,

preprint

A. Maaloui, A. Pinamonti, G. Speight Function Spaces via Fractional Poisson Kernel on Carnot Groups and Applications .preprint submitted for publication, ,

S. Eriksson-Bique, G. Giovannardi, R. Korte, N. Shanmugalingam, G. Speight Regularity of Solutions to the Fractional Cheeger-Laplacian on Domains in Metric Spaces of Bounded Geometry .preprint submitted for publication, ,

Invited Presentations

(03-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .Geometry Seminar, University of Jyvaskyla, Finland.

(01-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .Colloquium, University of Cincinnati, US.

(01-2015. ) Differentiability of Lipschitz Functions and Curves in Carnot Groups .University of Bath, UK.

(12-2013. ) Porosity and Differentiability .Leipzig, Germany.

(11-2013. ) Porosity and Differentiability .Analysis Seminar, Innsbruck, Austria.

(10-2013. ) Porosity and Differentiability .ERC Workshop on Geometric Measure Theory, Analysis in Metric Spaces and Real Analysis, Pisa, Italy.

(01-2013. ) Porosity and Differentiability .Albert Einstein Institute, Potsdam, Germany.

(01-2016. ) A Measure Zero Universal Differentiability Set in the Heisenberg Group .AMS Special Session on Analysis and Geometry in Nonsmooth Metric Measure Spaces, JMM 2016, Seattle, USA.

(03-2016. ) A Measure Zero Universal Differentiability Set in the Heisenberg Group .AMS Special Session on Geometric Measure Theory and Its Applications, AMS Spring 2016 Eastern Sectional Meeting, SUNY Stony Brook, USA.

(06-2016. ) Differentiability in Carnot Groups .University of Warwick, UK.

(06-2016. ) Lusin Approximation and Differentiability in Carnot Groups .Conference on Singular Phenomena and Singular Geometries, University of Pisa, Italy.

(10-2016. ) Differentiability of Lipschitz maps in Euclidean spaces and Carnot groups .Analysis Seminar, University of Illinois at Urbana-Champaign.

(03-2017. ) Porosity and Differentiability in Euclidean Spaces and Carnot Groups .Conference on Analysis on Metric Spaces, University of Pittsburgh.

(06-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .23rd Rolf Nevanlinna Conference, ETH Zurich, Switzerland.

(06-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .University of Trento, Italy.

(07-2017. ) Maximal directional derivatives and universal differentiability sets in Carnot groups .Geometric Measure Theory Conference, University of Warwick, UK.

(03-2018. ) Differentiability of Lipschitz Maps in Euclidean Spaces and Carnot Groups .Colloquium, Ball State University.

(09-2018. ) Fall Eastern Sectional Meeting, University of Delaware.

(10-2018. ) SIAM Central States Sectional Meeting, University of Oklahoma.

(02-2019. ) Workshop in Geometric Measure Theory, Johns Hopkins University.

(03-2019. ) AMS Spring Central and Western Joint Sectional Meeting, University of Honolulu.

(04-2019. ) AMS Spring Eastern Sectional Meeting, University of Connecticut.

(05-2019. ) Colloquium, Bowling Green State University.

(05-2019. ) Three Analysis Seminars, University of Trento, Italy.

(09-2019. ) AMS Fall Central Sectional Meeting, University of Wisconsin-Madison.

(11-2019. ) Latest in Geometric Analysis, Bedlewo, Poland.

2013 Warwick Faculty of Science Doctoral Thesis Award University of Warwick Status:Recipient

2013 Warwick Award for Teaching Excellence for Postgraduate Research Students Status:Nomination

Marco Capolli (PhD co-supervisor with Andrea Pinamonti) (Doctoral ) Status:In Progress

MathSciNet Mathematical Reviews Reviewer Type:Service to Professional Associations 2013 -To Present

International Mathematics Research Notices Peer Review/Referee

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze Peer Review/Referee

Bulletin of the London Mathematical Society Peer Review/Referee

(Master of Science Oral Exam Committee for Chris Foster (12/2015), Mehmet Ozdemir (12/2015), Brian Reid (04/2019) ) Member Type:Departmental Service Level:Department

Organizer of the UC Analysis and PDE Seminar Type:Departmental Service 2016 -To Present

(Visiting Assistant Professor Hiring Committee ) Member Type:Departmental Service 2016

(Graduate Student Evaluation Committee ) Member Type:Departmental Service 2016 -To Present

(Organizing Committee for the Ohio River Analysis Meeting (ORAM) ) Member Type:Departmental Service 2016 -To Present

(Executive Committee ) Member Type:Departmental Service 2016

(Graduate Advisor Committee ) Member Type:Departmental Service 2016 -To Present

(PhD Advanced Exam Committee for Rebekah Jones (12/2016), Abigail Richard (12/2016) and Hyogo Shibahara (TBA) ) Member Type:Departmental Service

(PhD Dissertation Committee for Rebekah Jones (04/2019), Abigail Richard (05/2019) and Hyogo Shibahara (TBA) ) Member Type:Departmental Service

National Science Centre (Poland) (External Grant Reviewer ) 03-2017

(Prelim Examination Committee (Real and Complex Analysis) ) Member Type:Departmental Service 2015 -2018

(Co-organizer (with Nageswari Shanmugalingam) of a special session on “Analysis and Geometry in Non-Smooth Spaces” at the AMS Spring Eastern Sectional Meeting 2018, Northeastern University, April 21-22, 2018 )

Cincy Math Circle Member Type:Community Service Level:Local 10-2017 -To Present

Journal d'Analyse Mathematique Peer Review/Referee

(Qualifying Exam Committee ) Member Type:Departmental Service 2017 -To Present

(Co-organizer (with Nageswari Shanmugalingam) of a Taft Research Seminar on Non-Smooth Analysis ) Type:Departmental Service 2019

Forum Mathematicum Peer Review/Referee 03-2018

(Co-organizer for a sectional meeting of the American Mathematical Society at the University of Cincinnati during April 17-18, 2021. ) Committee Member

(Applied for and awarded NSF funds to enable early career US mathematicians to attend the conference "Latest in Geometric Analysis" in Bedlewo, Poland during November 2019 )

(Grant Reviewer for the Simons Foundation ) 2019 -2019

(Prelim Examination Committee (Real Analysis) ) Committee Chair 2018 -To Present

09-2015 -To Present: American Mathematical Society

09-2015 -To Present: American Association of University Professors

REAL ANALYSIS

-MATH-1045 APPLIED CAL II Level:Undergraduate

-MATH-1061 CALCULUS I Level:Undergraduate

Geometric Analysis Level:Graduate

15-MATH-251 CALCULUS I Level:Undergraduate

-MATH-1062 CALCULUS II Level:Undergraduate

Advanced Calculus II Level:Both