The Mathematics Undergraduate Seminar
(II)

1st May 2025

UGS 2 Poster

The Second Undergraduate Seminar Session

The second session of UGS continued our exploration of mathematics across disciplines, featuring talks on protein structure determination, coding theory, and legendary mathematical problems.

Speakers & Topics

  • Loredana-Maria Iacob – Mathematics of Protein Structure Determination 18:30—19:05 Scientists lacked a clear understanding of how waves interact with atoms and crystals. Analysing diffraction peaks determines the spacing between atomic planes and, consequently, the crystal's structure. In this talk, we introduce Bragg's law in the context of X-ray Crystallography. We outline the protein structure determination by crystallization, Fourier analysis on diffraction intensities, and finally solving the electron density map. Even in a field where mathematics is assumably absent, this talk illustrates the power of mathematical construction and its unforeseen applicability to complex systems and real-world phenomena.
  • Aly Assaf – On the Problem of Reliable Communication: Shannon's Theorem and Polar Codes 19:30—20:05 Coding Theory is responsible for facilitating reliable message-passing over communication channels. In 1948, Claude Shannon proved that for every channel, there exists a family of error-correcting codes that allow reliable communication at any rate below the channel's capacity. This talk introduces the general Coding Theory scheme and outlines Shannon's key arguments. We explore Erdal Arikan's polar codes, the first constructive example to achieve Shannon's maximum capacity over symmetric binary-input memoryless channels—a discovery presenting a strong candidate for future 6G communication.
  • Vano Kakiashvili – The Legend of Question Six 20:10—20:45 The Legend of Problem 6 goes back to the 1988 International Mathematics Olympiad for high school students. The problem is so challenging that four brilliant number theorists could not solve it in six hours. Behind this problem lies a powerful and elegant technique known as Vieta Jumping, used to tackle Diophantine equations. Our goal is to explore the underlying ideas of Vieta Jumping, its strategic use in proofs by contradiction, and its role in unlocking unexpected symmetries. This talk offers both insight and inspiration for problem-solving.