Abdul Shabeer

PhD Student in Mathematics

Department of Mathematics, University of Iowa

I am a fifth-year PhD student working in the Department of Mathematics at the University of Iowa, advised by Prof. Mohammad Tehrani. My research area is broadly in the area of symplectic topology. Currently, I am studying the embeddability of symplectic four manifolds into six manifolds as hyperplane sections. Donaldson divisors are good examples of hyperplane sections. In particular, I am working with the ruled surfaces. This has applications in the Weinstein (or Stein) fillability of a class of contact manifolds called prequantum bundles.

I did an integrated bachelor's and master's degree at NISER, Bhubaneswar.

In my free time, I enjoy reading fantasy fiction, biking and playing pickleball.

✉ abdul-shabeer@uiowa.edu
🏛 MacLean Hall, Iowa City

Research

My primary area of research is symplectic topology. More precisely, I study symplectic embeddability of four manifolds into six manifolds as hyperplane sections. This has applications in the Weinstein (or Stein) fillability of a class of contact manifolds called prequantum bundles or Boothby-Wang bundles.

Papers & Preprints

Non-Embeddability of Ruled Surfaces as Symplectic Hyperplane Sections

In preparation

We show that certain ruled surfaces cannot be embedded as symplectic hyperplane sections of any closed integral symplectic manifold 6-manifold. It uses the moduli of J-holomorphic curves as a tool.

Talks

Aug 2026

Weinstein fillings of Prequantum Bundles

AMCS-Math Day · Univ of Iowa
May 2026

Non-Embeddability of Rational Ruled Surfaces as Symplectic Hyperplane Sections

GTA Philadelphia · Temple University
Mar 2026

Symplectic Isotopy Problem

Geometry and Topology Training Seminar · University of Iowa
Sept 2025

Non-Embeddability of Rational Ruled Surfaces as Symplectic Hyperplane Sections

AMCS-MATH Day · University of Iowa
Oct 2024

Stacks - Versal Families and Weierstrass Compactification

Geometry and Topology Training Seminar · University of Iowa
Feb 2024

Introduction to K3 Surfaces

Geometry and Topology Seminar · University of Iowa
Sept 2023

The Levi-Civita Connection

Geometry and Topology Seminar · University of Iowa
Mar 2023

Knot-Floer Homology: Filtration and Categorification

Geometry and Topology Seminar · University of Iowa

Teaching

Instructor of Record, University of Iowa

MATH:1850: Calculus I - Spr 2026

Topics: Fundamental concepts, limits, methods and techniques of differential calculus of a single variable; definite and indefinite integrals, substitution rule, fundamental theorem of calculus; applications including graphing, extreme values, areas, and volumes.
Syllabus · Sample Lecture Note · Sample Activity

MATH:1005: College Algebra - Fall 2024

Topics: Algebraic techniques, equations and inequalities, functions and graphs, exponential and logarithmic functions, systems of equations and inequalities.
Syllabus

MATH:1010: Trigonometry - Fall 2023; Spr 2024

Topics: Trigonometric functions, solutions of right and oblique triangles, trigonometric identities, complex numbers, and vectors.
Syllabus

Graduate Teaching Assistant, University of Iowa

MATH:1850: Calculus I - Spr2025; Fall 2026

Topics: Fundamental concepts, limits, methods and techniques of differential calculus of a single variable; definite and indefinite integrals, substitution rule, fundamental theorem of calculus; applications including graphing, extreme values, areas, and volumes.
Syllabus · Common Graphs

MATH:2850: Calculus III - Fall 2025

Topics: Multivariable calculus; vector functions, total differentials, gradient, implicit functions, coordinate systems, Taylor's expansion, extrema, multiple integrals, vector fields, line integrals, surface integrals, and Green's, Stokes', and divergence theorems.
Sample Quiz

MATH:1350: Quantitative Reasoning for Business - Fall 2022; Spr 2023

Topics: Algebraic techniques and modeling; quantitative methods for treating problems that arise in management and economic sciences; topics include algebra techniques, functions and functional models, exponential and logarithmic functions and models, and a thorough introduction to differential calculus; examples and applications from management, economic sciences, and related areas; for students planning to major in business.
Syllabus

Service

Interviewed Candidates for Undergraduate Positions in the Mathematics Tutorial Lab Aug 2026

I helped interview and evaluate several undergraduates applying for the tutoring positions at the Mathematics Tutorial Lab.
GradLife Peer-to-Peer Mentor · ISSS, Univ of Iowa Fall 2025 - Spr 2027

GradLife-P2P is the Graduate College’s interdisciplinary peer mentor matching program to help incoming international graduate students to settle into the program. I mentored a chemistry student during 2025-2026 and two students from the Psychology program during 2026-2027.
Directed Reading Program (DRP) Spr, Fall 2026

Mentored an undergraduate student in logic and introduction to proofs through a reading project. We met once a week and discussed the math.
Travel Funding Committee Member- Math Graduate Board (MGB), Univ of Iowa 2026

The Travel Funding Committee reviews funding applications from graduate students for travel to confer ences and workshops.
Math Department First Year Buddy Program Fall 2023

Mentored an incoming math graduate student in managing their academic and social life, and teaching duties.