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This is a sample blog post. Lorem ipsum I can’t remember the rest of lorem ipsum and don’t have an internet connection right now. Testing testing testing this blog post. Blog posts are cool.
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portfolio
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publications
List Distinguishing Number of Power of Hypercube and Cartesian Powers of a Graph
Published in CALDAM, 2020
This symmetry breaking coloring property is studied for certain special classes of graphs
Contrasting the Halves of an Ahmad Pair
Published in submitted., 2025
We show that the left half has to be low_3 while the right half is high_2
talks
Characterizing Ahmad pairs in the local structure
Published:
A pair (A,B) of Σ2-sets forms an Ahmad pair if every set strictly below A is also below B. We give a characterization for when a set can be the left half of an Ahmad pair. We also introduce a hierarchy of Ahmad n-pairs in the local structure and characterize them using different notions of join irreducibility. The eventual goal is to come up with a property separating the two halves of an Ahmad pair.
Separating the halves of an Ahmad pair
Published:
Incomparable Σ02 sets (A,B) form an Ahmad pair if every set strictly enumeration below A is also enumeration below B. Extending previous work, in this talk we will characterize the left halves of Ahmad pairs as precisely the low3 and join irreducible sets and show that the right halves cannot be low3 thereby giving a natural separation between the two halves. Slides
Constrasting the halves of an Ahmad Pair
Published:
We study Ahmad pairs in the Σ02 enumeration degrees. We say (A,B) form an Ahmad pair if A ≰e B and every Z <e A satisfies Z ≤e B. Ahmad pairs have recently drawn interest as they are a key obstacle in solving the AE theory of the local structure.
Enumeration Degrees - Local and Global Structure
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he local structure of the e-degrees refers to the e-degrees below 0’. These correspond precisely to the degrees of the \Sigma_2 sets. We shall talk about enumeration reducibility, its connection to Turing reducibility as well as contrast the local structure of the e-degrees with that of the Turing degrees. After a survey of known results we shall end with our new work and some open questions.
teaching
Calculus and Analytic Geometry 2 - MATH222
UW-Madison
Lecturer for summer term 2025.
Calculus and Analytic Geometry 1 - MATH221
UW-Madison
TA Fall 23.
Linear Algebra - MATH340
UW-Madison
TA Spring 25
Multivariable Calculus - MATH234
UW-Madison
TA Fall 22, TA Spring 23, Head TA Spring 24.
Preparatory Algebra - MATH96
UW-Madison
Instructor for pre-calculus algebra, Fall 24 and Fall 25.
Grading Duties
UW-Madison
Grader for graduate logic classes MATH770 (Foundations of Math), MATH771 (Set Theory), MATH773 (Computability Theory) and undergraduate classes MATH522 (Analysis 2), MATH475 (Intro Combinatorics), MATH567 (Modern Number Theory)