PhD Student

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email:

blog:

phone: 61 2 6125 5982

Welcome to my ANU page. You may find it a useful indication of what I do around the university.

Above this text, you can see a photo of a budding mathematician in need of a good haircut.

If you click this link, you can hear a song I recorded about maths some years ago.

NEWS: I am in the process of finishing up and moving to Sydney to start work. Please use awdudek[at]gmail.com to contact me.

Candidacy

Since November of 2012, I have been studying for a PhD under the supervision of Dr Timothy Trudgian at the Australian National University. My research is in analytic number theory, particularly the Riemann zeta-function and its tender romance with the distribution of the prime numbers. I sometimes take a dip into graph theory and other fun things. My explorations are kindly supported by an Australian Postgraduate Award and an ANU Supplementary Scholarship.

Thesis

I am currently writing my PhD thesis, which is essentially a collection of some of my publications from below.

Publications

1. Almost-Ramanujan Graphs and Prime Gaps, European J. Combin., 2015 (43) 204-209

2. On the Riemann Hypothesis and the Difference Between Primes, Int. J. Number Theory, 2015

3. An Explicit Result for $|L(1+it, \chi)|$, (to appear) Funct. Approx. Comment. Math., 2015

4. (with D. Platt) On Solving a Curious Inequality of Ramanujan, (to appear) Exp. Math., 2015

5. On the Sum of a Prime and a Square-free Number, (to appear) Ramanujan J., 2015

6. Corrigendum to “Almost-Ramanujan Graphs and Prime Gaps”, (to appear) European J. Combin., 2015

7. (with L. Grenie and G. Molteni) Primes in Explicit Short Intervals on RH, (to appear) Int. J. Number Theory, 2015

8. On the Number of Divisors of $n^2-1$, (to appear) Bull. Aust. Math. Soc., 2015

9. (with D. Platt) On the Sum of the Square of a Prime and a Square-free Number, (to appear) LMS J. Comput. Math., 2015

10. On the Spectrum of the Generalised Petersen Graphs, (to appear) Graphs Combin., 2015

Submitted

1. An Explicit Result for Primes Between Cubes, Preprint, 2014

2. A New Proof of Euclid’s Theorem, Preprint, 2015

3. On the Distribution of Products of Primes and Powers, Preprint, 2015

I enjoy maths, football (spherical, not ellipsoidal), reading, chess, poker and long romantic walks on the beach.

Some articles for The Conversation

1.     (8/4/13)

2.     (10/4/13)

3.     (13/6/13)

4.     (12/8/13)

5.     (30/8/13)

Teaching

·       Semester 2 2015: Tutor for MATH3301 Number Theory and Cryptography (ANU)

·       Semester 1 2015: Tutor for MATH1115 Mathematics and Applications 1 Honours (ANU)

·       Semester 2 2014: Tutor for MATH3301 Number Theory and Cryptography (ANU)

·       Semester 1 2014: Tutor for MATH1115 Mathematics and Applications 1 Honours (ANU)

·       Semester 2 2013: Tutor for MATH1013 Mathematics and Applications 1 (ANU)

·       Semester 1 2013: Tutor for MATH1115 Mathematics and Applications 1 Honours (ANU)

Curriculum Vitae

Outreach

I work with ANU Student Equity as a Senior Community Maths Ambassador. This involves visiting disadvantaged high schools and getting the students excited about maths. If you’re a student who is interested in doing this, you should send me an email.

A photo

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