I am an R. H. Bing Fellow in the Department of Mathematics at The University of Texas at Austin.
Previously, I was a member of the Geometric Analysis group at the Warwick Mathematics Institute since between September 2019 and August 2025.
I completed my PhD in the Warwick Mathematics Institute at the University of Warwick under the guidance of Prof. Peter M. Topping in September 2024. My PhD thesis, entitled Geometric regularity properties of the Curve Shortening Flow, was awarded a Science, Engineering and Medicine Faculty Thesis Prize.
I complete my Bachelors and Masters at Queens' College, University of Cambridge, during which time I was awarded a Foundation Scholarship.
After removing all capital z's, I can be contacted at arjZun.sZobnZack@ausZtinZ.uteZxasZ.edu.
My research interests lie within the intersection of Differential Geometry and Partial Differential Equations, more specifically in the field of Geometric Flows. My completed work has thus far concerned the Curve Shortening Flow, a geometric flow of properly embedded curves which arises as a gradient flow of the length functional. My research has been primarily centred around uncovering parabolic estimates for the Curve Shortening Flow starting from weak initial assumptions, in particular those with simple geometric interpretations.
Differential Geometry
Partial Differential Equations
Geometric Flows
Geometric and Non-linear Partial Differential Equations
Geometric Analysis
(joint with P. M. Topping) The Harnack inequality without convexity for curve shortening flow. In preparation, Aug. '25+.
A delayed interior area-to-height estimate for the Curve Shortening Flow. Preprint, arXiv:2502.16581, Feb. '25.
(joint with P. M. Topping) Monotonicity of the modulus under curve shortening flow. Preprint, arXiv:2409.03098, Sep. '24.
(joint with P. M. Topping) Delayed parabolic regularity for curve shortening flow. Preprint, arXiv:2408.04049, Aug '24.
Delayed parabolic regularity for the curve shortening flow.
UT Knoxville Geometric Analysis Seminar, Nov. '25
Rutgers Geometric Analysis Seminar, Nov. '25
UT Austin Analysis Seminar, Sep. '25
Technische Universität Darmstadt AG-Seminare, May '25.
King's College London Analysis Seminar, Jan. '25.
Warwick Analysis Seminar, Jan. '25.
Leeds Geometry Seminar, Oct. '24.
Warwick Mathematics Postgraduate Seminar, Oct. '24.
An introduction to Geometric PDEs via the Bernstein Problem.
Warwick Junior Analysis Seminar, Mar. '24.
Warwick Online Mathematics Postgraduate Seminar, Feb. '21.
The Gage–Grayson–Hamilton Theorem.
Mean Curvature Flow Reading Seminar, Jul. '21.
The Łojasiewicz Inequalities.
Warwick Mathematics Postgraduate Seminar, Jan. '20.
Warwick Imperial Autumn Meeting, Nov. '19.
Curvature and Global Shape. Universität Münster, Jul.–Aug. '25.
Topics in Geometric Analysis. Centro Ennio De Giorgi, Pisa, Jun. '25.
Third Meeting of the UK Metric Geometry and Analysis Network. St. Hilda's College, University of Oxford, Apr. '25.
Geometric Flows and Applications. ICMS Bayes Centre, Edinburgh, Jul. '23.
British Mathematical Colloquium 2023. University of Bath, Apr. '23.
Ricci flow and related topics. University of Warwick, Mar. '23.
Geometric Partial Differential Equations. University of Warwick, Dec. '22.
International PDE Conference. University of Oxford, Jul. '22.
Geometric Flows. IACM Institute, Crete, Jun.–Jul. '22.
British Mathematical Colloquium 2022. King’s College London, Jun. '22.
(online) New Directions in Geometric Flows. Banff International Research Station, Nov. '21.
(online) Curvature Constraints and Spaces of Metrics. Institut Fourier, France, Jun.–Jul. '21.
Advanced in Geometric Analysis. L’Université Paris-Diderot, Dec. '19.
Brussels-London 19: Ricci Flow. Queen Mary University of London, Dec. '19.
Class Instructor.
M 408D: Sequences, Series, and Multivariable Calculus.
Teaching Fellow. My responsibilities include providing:
teaching of all core modules to and pastoral care for 10 first-year students
pastoral care and essay supervision in a range of topics for 5 second-year students
pastoral care and references for 8 third- and fourth-year students
running support workshops in core second-year modules for all undergraduates
running weekly classes for (fourth year) Hyperbolic Geometry and Advanced Real Analysis
exam marking.
Teaching Assistant. I have presented weekly support classes for the following modules
(first year) Analysis II
(second year) Analysis III, Multivariable Analysis
(third year) Complex Analysis, Functional Analysis I, Functional Analysis II, Geometry of Curves and Surfaces, Manifolds, Measure Theory
(fourth year) Advanced PDEs, Differential Geometry
Peer Tutor for the Analysis I
Supervisor. I have supervised (small-group teaching, including marking) first-year students in
(at Warwick) All core modules
(at Cambridge) Groups
Tutor. I have tutored over 20 students and pupils in their Bachelor, STEP, A-Level, GCSE and Key Stage 9 studies.
Marker. I have marked exams for
(first year) Analysis I, Analysis II
(second year) Analysis III, Methods of Mathematical Modelling III, Theory of ODEs
(third year) Complex Analysis, Functional Analysis I, Theory of PDEs
Warwick Analysis Seminar. I co-organised said seminar. University of Warwick, Apr.–Jun. '25.
Graduate Teaching Assistant Teaching Prize. I was awarded said prize in recognition of my contribution to teaching in the department. University of Warwick, Jul. '24.
Staff and Graduate Student Liaison Committee. I held the position of secretary for said committee. My responsibilities included collecting feedback from the graduate student community concerning the running of the department and co-organising events for graduate students, in particular the Christmas party. Some of my successes include co-introducing a social Easter event and co-opening most of the social events to the wider mathematics department. University of Warwick, Oct. '21–May '22.
Warwick Online Mathematics Postgraduate Seminar. I co-organised said seminar, and co-introduced an online social aspect during COVID. University of Warwick, Oct. '20–Jun. '21.
The Cyril Bibby Prize. I was awarded said prize for making "an outstanding contribution ... to the general communal life of the college". Queens' College, University of Cambridge, Sep. '18.
Queens' College Access Programme. I was heavily involved in the outreach programme, whose aim is to encourage potential students from underprivileged backgrounds to consider the University of Cambridge for their further education. My roles included giving numerous tours of Queens' College to potential applicants from underprivileged schools/communities, in order to encourage them to apply to top universities, and attending two voluntary week-long tours to visit underprivileged schools, in Kent and in London. Queens' College, University of Cambridge, Oct. '15–Jun. '18.