Abdul Basit
Visiting Assistant Professor at University of Notre Dame
Visiting Assistant Professor, Department of Mathematics, University of Notre Dame
I'm a computer scientist specializing in algorithm design, discrete geometry and graph theory. I have over five years of software development experience using Python, Java, and PHP. My current interests include machine learning and big data.
University of Notre Dame
https://www.linkedin.com/company/university-of-notre-dame
Research:
- Conduct research in Extremal & Probabilistic Combinatorics, and Model Theory.

Teaching: 
- Courses: Basic Combinatorics, Polynomial Methods in Combinatorics, Finite Mathematics
- Responsible for planning, organizing, teaching and grading.
South Bend, Indiana Area
https://media-exp1.licdn.com/dms/image/C4E0BAQG6VvWuWHam-Q/company-logo_100_100/0/1621860696895?e=1655942400&v=beta&t=kIUANgc_Xz5ZGMj3pYjnFIbd30RkQuXpLtAHQARUFcU
Visiting Assistant Professor
Independent Software Development Consultant
https://www.linkedin.com/company/independent-software-development-consultant
- Built, implemented and maintained many user-friendly web applications & back-end services using Python and PHP, demonstrating focus on client’s needs and shipping working code.
- Built web crawlers and data processing software.
Software Development Consultant
Rutgers University–New Brunswick
https://www.linkedin.com/company/rutgersnb
Research Assistant: 
- Conducted original research in Discrete & Computational Geometry, and Additive Combinatorics.
- Resulting publications:
       "Incidences with k-non-degenerate sets and their applications", 
       "On the number of ordinary lines determined by sets in complex space",
       "An improved sum-product bound for quaternions"

Teaching Assistant:
- Courses: Computational Geometry, Graduate Algorithms, Foundations of Computer Science, Numerical Analysis,  Discrete Structures II, Undergraduate Algorithms, Introduction to Computer Science
- Responsible for tutorial sessions, preparing and grading quizzes and exams.
Greater New York City Area
https://media-exp1.licdn.com/dms/image/C4D0BAQFeNRn2kP_UhA/company-logo_100_100/0/1615313451175?e=1655942400&v=beta&t=idyKBVTTCHKNWogaQZ1kNiXurSRP3IKPBg5iUYxRc3w
Graduate Research And Teaching Assistant
Lahore University of Management Sciences
https://www.linkedin.com/company/lahore-university-of-management-sciences
Research Assistant: 
- Conducted original research in Combinatorial Geometry.
- Resulting publications:
        "Hitting Simplices with Points in Euclidean Space",
        "Centerpoints and Tverberg’s Technique".

Teaching Assistant:
- Courses: Advanced Algorithms, Computational Biology, Computer Networks, Network Protocols and Standards, Object Oriented Programming:
- Responsible for tutorial sessions, preparing and grading quizzes and exams.
https://media-exp1.licdn.com/dms/image/C4E0BAQFW9AiCxBrPwg/company-logo_100_100/0/1519871792235?e=1655942400&v=beta&t=a_zHPRJ91hz6w4HpbgMj8XaVfU13_R8rHSgUiaTZI4A
Research And Teaching Assistant
Confiz Solutions
https://www.linkedin.com/company/confiz
- Worked on several user facing features for a media streaming web application, Urfilez. (PHP, MySQL, Linux)
https://media-exp1.licdn.com/dms/image/C4D0BAQHnyQFhNgcH9g/company-logo_100_100/0/1632220167704?e=1655942400&v=beta&t=oeJ1E0iOe38cAqzBFCInI9ng2iGX8RG59Q1psPShTTc
Software Engineer
PhD
Ph.D. in Computer Science focusing on Discrete & Computational Geometry, advised by William Steiger.
− Dissertation title: Some applications of algebraic methods in combinatorial geometry.
Computer Science
https://media-exp1.licdn.com/dms/image/C4D0BAQFeNRn2kP_UhA/company-logo_100_100/0/1615313451175?e=1655942400&v=beta&t=idyKBVTTCHKNWogaQZ1kNiXurSRP3IKPBg5iUYxRc3w
Rutgers University–New Brunswick
https://www.linkedin.com/school/rutgersnb/
B.Sc.
Computer Science
https://media-exp1.licdn.com/dms/image/C4E0BAQFW9AiCxBrPwg/company-logo_100_100/0/1519871792235?e=1655942400&v=beta&t=a_zHPRJ91hz6w4HpbgMj8XaVfU13_R8rHSgUiaTZI4A
Lahore University of Management Sciences
https://www.linkedin.com/school/lahore-university-of-management-sciences/
Kelly's theorem states that a set of n points affinely spanning C^3 must determine at least one ordinary complex line (a line passing through exactly two of the points). Our main theorem shows that such sets determine at least 3n/2 ordinary lines, unless the configuration has n−1 points in a plane and one point outside the plane (in which case there are at least n−1 ordinary lines). In addition, when at most 2n/3 points are contained in any plane, we prove a theorem giving stronger bounds that take advantage of the existence of lines with 4 and more points (in the spirit of Melchior's and Hirzebruch's inequalities). Furthermore, when the points span 4 or more dimensions, with at most 2n/3 points contained in any three dimensional affine subspace, we show that there must be a quadratic number of ordinary lines.
On the number of ordinary lines determined by sets in complex space
Discrete & Computational Geometry
https://link.springer.com/article/10.1007/s00454-018-0039-4
We show that there exists an absolute constant c > 0, such that, for any finite set A of
quaternions, max{|A + A, |AA|} ≥ |A|^{4/3+c}. This generalizes a sum-product bound for real numbers proved by Konyagin and Shkredov.
An improved sum-product bound for quaternions
September 6, 2018
https://arxiv.org/abs/1809.02214
We study point-sphere and point-plane incidences in the three-dimensional space. In particular, for 1<k<n, we say that a set of spheres (resp., of planes) is k-non-degenerate if no circle is contained in k spheres of the set (resp., if no line is contained in k planes of the set). We prove that, for every ε>0, the number of incidences between a set of m points and a k-non-degenerate set of n spheres is O(m^{3/4+ε}n^{3/4}k^{1/4}+n+mk). Similarly, we prove that, for every ε>0, the number of incidences between a set of m points and a k-non-degenerate set of n planes is O(m^{4/5+ε}n^{3/5}k^{2/5}+n+mk).
These bounds are obtained by using the polynomial partitioning technique, recently introduced by Guth and Katz. More specifically, in our proofs we use a pair of constant-degree partitioning polynomials.

We also present a couple of applications of k-non-degenerate sets:
(i) We consider an extension of the three-dimensional unit distances problem, in which we are given a set D of k distinct distances and ask for a three-dimensional set of m points that maximizes the number of pairs of points that span a distance from D. By relying on k-non-degenerate sets of spheres, we prove an upper bound of O(m^{236/149+ε}k^{125/149}) for the problem (which improves the trivial bound for large values of k).
(ii) We consider the maximum number of incidences between a three-dimensional set of n planes (without any restrictions) and a set of m points, such that no k points are collinear. Our bound for k-non-degenerate planes immediately implies a bound of O(n^{4/5+ε}m^{3/5}k^{2/5}+m+nk) for this problem, generalizing the previous bound O(n^{4/5}m^{3/5}+nlogm) for the specific case where no three points are collinear (up to the ε in the exponent).
Incidences with k-non-degenerate sets and their applications
Journal of Computational Geometry
http://www.jocg.org/index.php/jocg/article/view/138
The so-called first selection lemma states the following: given any set P of n points in R^d, there exists a point in ℝ d contained in at least c_d n^{d+1} − O(n^d) simplices spanned by P, where the constant c_d depends on d. We present improved bounds on the first selection lemma in R^3. In particular, we prove that c_3 ≥ 0.00227, improving the previous best result of c_3 ≥ 0.00162 by Wagner (On k-sets and applications. Ph.D. thesis, ETH Zurich, 2003). This makes progress, for the three-dimensional case, on the open problems of Bukh et al. (Stabbing simplices by points and flats. Discrete Comput. Geom., 2010) (where it is proven that c_3 ≤ 1/44 ≈ 0.00390) and Boros and Füredi (The number of triangles covering the center of an n-set. Geom. Dedic. 17(1):69–77, 1984) (where the two-dimensional case was settled).
Hitting Simplices with Points in R^3.
Discrete & Computational Geometry
https://link.springer.com/article/10.1007/s00454-010-9263-2
Using a technique that Tverberg and Vrecica (1993) discovered to give a surprisingly simple proof of Tverberg's theorem, we show the following extension of the centerpoint theorem. Given any set P of n points in the plane, and a parameter 1/3 ≤ c < 1, one can always find a disk D such that any closed half-space containing D contains at least cn points of P. Furthermore, D contains at most  points of P (the case c = 1 is trivial – take any D containing P; the case c = 1/3 is the centerpoint theorem). We also show that, for all c, this bound is tight up to a constant factor. We extend the upper bound to . Specifically, we show that given any set P of n points, one can find a ball D containing at most ((d+1)c-1)n/d points of P such that any half-space containing D contains at least cn points of P.
Centerpoints and Tverberg’s Technique
Computational Geometry
https://www.sciencedirect.com/science/article/pii/S0925772110000131
The program at Institute for Pure Applied Mathematics in Los Angeles at the University of California, Los Angeles brought together researchers working in Combinatorial Geometry for a period of 4 months to foster collaboration and exchange of ideas.
-
Core Participant in Program on Algebraic Techniques for Combinatorial and Computational Geometry
-
Excellence Fellowship at Rutgers University
Algebraic Gems of Theoretical Computer Science
-
Analysis of Boolean Functions
-
Arithmetic Combinatorics
-
Combinatorics I
-
Combinatorics II
-
Computational Complexity
-
Computational Geometry
-
Database Systems
-
Design & Analysis of Algorithms I
-
Design & Analysis of Algorithms II
-
Error Correcting Codes
-
Extremal Combinatorics
-
Foundations of Computer Science
-
Graph Theory
-
Principles of Artificial Intelligence
-
Probabilistic Combinatorics
-
Topics in Complexity and Pseudorandomness
-
Topics in Discrete Geometry
-
Topics in Finite Fields
-
https://pk.linkedin.com/in/basit-shariq-14b047208
Karāchi
Basit Shariq
--
https://ca.linkedin.com/in/masoomeh-akbari-659406201
Ottawa, ON
Masoomeh Akbari
Research Assistant at University of Ottawa
https://ca.linkedin.com/in/kianoosh-shokri-0b8699a8
Ottawa, ON
Kianoosh Shokri
PHD student at uOttawa
https://www.linkedin.com/in/aishwarya-dahiwale
Pasadena, CA
Aishwarya Dahiwale
Astronomical Data Analyst at Caltech
https://ca.linkedin.com/in/mmollon
Toronto, ON
Matt Mollon
Senior Software Engineer at Venngage
https://pk.linkedin.com/in/imransarwar3
Pakistan
Imran Sarwar
Leadership | Innovation | Community
https://ca.linkedin.com/in/nazaninzaker
Canada
Nazanin Zaker, Ph.D.
Part-time professor at University of Ottawa
https://ca.linkedin.com/in/mavra-zehra-
Etobicoke, ON
Mavra Zehra
Evaluation l Research l Learning l Atlas Corps Fellow
https://www.linkedin.com/in/mahdtauseef
Greater Seattle Area
Mahd Tauseef
Software Engineer at Google
https://in.linkedin.com/in/balu-nagarajan-48a49b148
Chennai
Balu Nagarajan
Associate Vice President at TATA Capital Housing Finance Limited
https://www.linkedin.com/in/aneeqcheema
Greater Houston
Aneeq Cheema
Consultant to Gates Foundation - Health Systems Strengthening & Immunization
https://ae.linkedin.com/in/gauravrustagi
United Arab Emirates
Gaurav Rustagi
Shopper & Customer Marketing Director, Arabia at Unilever
https://pk.linkedin.com/in/yasserbashir
Pakistan
Yasser Bashir
Co-founder and Chief Executive Officer at Arbisoft.
https://in.linkedin.com/in/varunalagh84
Gurgaon
Varun Alagh
Co-Founder, CEO, Building brands for Millennials
https://pk.linkedin.com/in/afia-zafar-30b721122
Pakistan
Afia Zafar
Sr. Software Developer
https://pk.linkedin.com/in/khalida-ahson-866aa817
Lahore District
Khalida Ahson
Research & Development
https://ca.linkedin.com/in/shaheer-khan-bb222815
Calgary, AB
Shaheer Khan
Campus Principal | Teacher
https://pk.linkedin.com/in/mehboob-khan-746b3074
Lahore District
Mehboob Khan
Boston University School of Law
https://ca.linkedin.com/in/muradhassan
Greater Toronto Area, Canada
Hassan Murad
Tech Enabler, SAP techno functional, problem solver and passionate to build tools to drive efficiency. Change specialist for digital transformation and adoption
https://pk.linkedin.com/in/bretech
Pakistan
Abdul Basit
BreTech
https://ae.linkedin.com/in/abdul-basit-86630921
United Arab Emirates
Abdul Basit
Chief of Business Reporters
Khaleej Times
https://uk.linkedin.com/in/abdul-basit-670651b0
London
Abdul Basit
Abdul at HUGO BOSS
https://pk.linkedin.com/in/abdulbasit04
Pakistan
Abdul Basit
Assistant Marketing Manager - Indus Motors | Toyota Pakistan
https://sa.linkedin.com/in/abdul-basit-6298b552
Riyadh, Saudi Arabia
Abdul Basit
Accounts Payable Specialist /SAP HANA/ at Arabian Diagnostic and Medical Co  (FAL Holdings)