I am a final year PhD student in Mathematics at the University of Bristol. I work on the intersection between random matrix theory and analytic number theory.
Areas of Interest: Averages of Characteristic Polynomials, Logarithmic Derivative of the Riemann Zeta, L-functions.
Publications/Preprints:
- Averages of Long Dirichlet Polynomials for the Logarithmic Derivative (S. Baluyot, B. Conrey, A. Irfan and N.C. Snaith). PDF
- Sums of von Mangoldt convolutions via trace sums averages over U(N) (A. Irfan). PDF
- Averages of Traces over the Unitary Group (A. Irfan). PDF
- Moments of the Logarithmic Derivative of Characteristic Polynomials over U(N) (S. Baluyot, B. Conrey, A. Irfan and N.C. Snaith). PDF
- Zero-Error Superposition Codes (C. Wang; A. Irfan; Y. Zhang; M. Langberg; S. Jaggi). PDF (Also available at https://ieeexplore.ieee.org/document/11195672)
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Averages of Long Dirichlet Polynomials
Based on the work of Sandro Bettin and Brian Conrey, our paper extends the methods that were originally used for moments of the zeta function and variance of the k-fold divisor function to the logarithmic derivative of zeta. It uses the correspondence with Random Matrix Theory, where the characteristic polynomials of unitary matrices have served…
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Runway Funding from University of Bristol!
Recently, the University of Bristol provided significant funding for the Naru Maths app. With this funding, we will be able to train a pedagogical LLM that is designed specifically on the GCSE Curriculum. We have started with a revision on the logo and re-uploading the app on the App Store. Currently, the app has 80,000+…
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Collaboration Magic
The magic that emerges from effective collaboration is undeniable. When diverse minds converge with a shared purpose, the results can be transformative.
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Teamwork Triumphs
What fosters effective teamwork? It’s not just about grouping individuals together and hoping for the best. It’s about cultivating an environment where trust, open communication, mutual respect, and a shared vision converge.
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Adaptive Advantage
In an ever-shifting business landscape, adaptability isn’t just a trait—it’s a competitive advantage. Companies that embrace change, learn from challenges, and pivot when necessary are the ones that not only survive but also thrive in uncertain environments.
