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
Visiting Assistant Professor
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
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Independent Software Development Consultant
https://www.linkedin.com/company/independent-software-development-consultant
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.
Rutgers University–New Brunswick
https://www.linkedin.com/company/rutgersnb
Graduate Research And Teaching Assistant
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
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Lahore University of Management Sciences
https://www.linkedin.com/company/lahore-university-of-management-sciences
Research And Teaching Assistant
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.
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Confiz Solutions
https://www.linkedin.com/company/confiz
Software Engineer
- Worked on several user facing features for a media streaming web application, Urfilez. (PHP, MySQL, Linux)
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Computer Science
PhD
Rutgers University–New Brunswick
https://www.linkedin.com/school/rutgersnb/
Ph.D. in Computer Science focusing on Discrete & Computational Geometry, advised by William Steiger.
− Dissertation title: Some applications of algebraic methods in combinatorial geometry.
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Computer Science
B.Sc.
Lahore University of Management Sciences
https://www.linkedin.com/school/lahore-university-of-management-sciences/
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On the number of ordinary lines determined by sets in complex space
Discrete & Computational Geometry
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.
https://link.springer.com/article/10.1007/s00454-018-0039-4
An improved sum-product bound for quaternions
September 6, 2018
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.
https://arxiv.org/abs/1809.02214
Incidences with k-non-degenerate sets and their applications
Journal of Computational Geometry
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).
http://www.jocg.org/index.php/jocg/article/view/138
Hitting Simplices with Points in R^3.
Discrete & Computational Geometry
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).
https://link.springer.com/article/10.1007/s00454-010-9263-2
Centerpoints and Tverberg’s Technique
Computational Geometry
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.
https://www.sciencedirect.com/science/article/pii/S0925772110000131
Core Participant in Program on Algebraic Techniques for Combinatorial and Computational Geometry
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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.
Excellence Fellowship at Rutgers University
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Algebraic Gems of Theoretical Computer Science
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Analysis of Boolean Functions
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Arithmetic Combinatorics
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Combinatorics I
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Combinatorics II
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Computational Complexity
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Computational Geometry
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Database Systems
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Design & Analysis of Algorithms I
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Design & Analysis of Algorithms II
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Error Correcting Codes
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Extremal Combinatorics
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Foundations of Computer Science
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Graph Theory
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Principles of Artificial Intelligence
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Probabilistic Combinatorics
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Topics in Complexity and Pseudorandomness
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Topics in Discrete Geometry
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Topics in Finite Fields
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https://pk.linkedin.com/in/basit-shariq-14b047208
Basit Shariq
--
Karāchi
https://ca.linkedin.com/in/masoomeh-akbari-659406201
Masoomeh Akbari
Research Assistant at University of Ottawa
Ottawa, ON
https://ca.linkedin.com/in/kianoosh-shokri-0b8699a8
Kianoosh Shokri
PHD student at uOttawa
Ottawa, ON
https://www.linkedin.com/in/aishwarya-dahiwale
Aishwarya Dahiwale
Astronomical Data Analyst at Caltech
Pasadena, CA
https://ca.linkedin.com/in/mmollon
Matt Mollon
Senior Software Engineer at Venngage
Toronto, ON
https://pk.linkedin.com/in/imransarwar3
Imran Sarwar
Leadership | Innovation | Community
Pakistan
https://ca.linkedin.com/in/nazaninzaker
Nazanin Zaker, Ph.D.
Part-time professor at University of Ottawa
Canada
https://ca.linkedin.com/in/mavra-zehra-
Mavra Zehra
Evaluation l Research l Learning l Atlas Corps Fellow
Etobicoke, ON
https://www.linkedin.com/in/mahdtauseef
Mahd Tauseef
Software Engineer at Google
Greater Seattle Area
https://in.linkedin.com/in/balu-nagarajan-48a49b148
Balu Nagarajan
Associate Vice President at TATA Capital Housing Finance Limited
Chennai
https://www.linkedin.com/in/aneeqcheema
Aneeq Cheema
Consultant to Gates Foundation - Health Systems Strengthening & Immunization
Greater Houston
https://ae.linkedin.com/in/gauravrustagi
Gaurav Rustagi
Shopper & Customer Marketing Director, Arabia at Unilever
United Arab Emirates
https://pk.linkedin.com/in/yasserbashir
Yasser Bashir
Co-founder and Chief Executive Officer at Arbisoft.
Pakistan
https://in.linkedin.com/in/varunalagh84
Varun Alagh
Co-Founder, CEO, Building brands for Millennials
Gurgaon
https://pk.linkedin.com/in/afia-zafar-30b721122
Afia Zafar
Sr. Software Developer
Pakistan
https://pk.linkedin.com/in/khalida-ahson-866aa817
Khalida Ahson
Research & Development
Lahore District
https://ca.linkedin.com/in/shaheer-khan-bb222815
Shaheer Khan
Campus Principal | Teacher
Calgary, AB
https://pk.linkedin.com/in/mehboob-khan-746b3074
Mehboob Khan
Boston University School of Law
Lahore District
https://ca.linkedin.com/in/muradhassan
Hassan Murad
Tech Enabler, SAP techno functional, problem solver and passionate to build tools to drive efficiency. Change specialist for digital transformation and adoption
Greater Toronto Area, Canada
Abdul Basit
https://pk.linkedin.com/in/bretech
BreTech
Pakistan
Abdul Basit
https://ae.linkedin.com/in/abdul-basit-86630921
Chief of Business Reporters
Khaleej Times
United Arab Emirates
Abdul Basit
https://uk.linkedin.com/in/abdul-basit-670651b0
Abdul at HUGO BOSS
London
Abdul Basit
https://pk.linkedin.com/in/abdulbasit04
Assistant Marketing Manager - Indus Motors | Toyota Pakistan
Pakistan
Abdul Basit
https://sa.linkedin.com/in/abdul-basit-6298b552
Accounts Payable Specialist /SAP HANA/ at Arabian Diagnostic and Medical Co  (FAL Holdings)
Riyadh, Saudi Arabia