The very-first undergraduate seminar displayed three motivated speakers. To them, we extend our gratitude for
the amazing talks!
Speakers & Topics
Klesta Qehaja – Random Walks on ℤᵈ19:00—19:30"A drunk man will find his way home, but a drunk bird may get lost forever" —
why does dimension dictate destiny? This intriguing observation lies at the heart of random walks, a
fundamental concept bridging probability, physics, and real-world phenomena. In this talk, we explore how
the behavior of random walks shifts dramatically with dimensionality. We sketch a proof of this dichotomy,
linking combinatorial intuition to deeper mathematical principles. Beyond theory, we highlight
applications—from stock market modeling to reveal how random walks underpin unpredictability in financial
systems.
Klesta Qehaja presenting Random Walks on ℤᵈ
Exploring the mathematics of random walks
Ahmed Maghri – Shor's Quantum Algorithm20:00—20:30Shor's algorithm presents a polynomial-time quantum solution to the integer
factorization problem, threatening classical encryption protocols like RSA. We introduce the mathematical
and computational foundations required to understand the algorithm, including modular arithmetic,
continued fractions, and quantum principles. We then provide a step-by-step breakdown of Shor's algorithm
and its quantum subroutine, emphasizing accessibility and conceptual clarity, while also addressing
practical constraints in current quantum hardware.
Ahmed Maghri presenting Shor's Quantum Algorithm
Explaining quantum computing principles
Breaking down the algorithm step-by-step
Pablo Santos Guerrero – On the Piccard—Vessiot Theory of Differential Equations20:30—21:00This talk focuses on the convenience of combining Algebraic Geometry to study
differential equations. The statement of interest is Liouville's Theorem, regarding the general solutions
of Linear Differential systems. We demonstrate how solutions to linear differential equations generate
field extensions and how their symmetries are captured by linear algebraic groups. Just as Galois
revolutionized algebra with his work, this talk is an invitation to share the regard for algebra and its
usefulness in many areas of mathematics.
Pablo Santos Guerrero presenting Piccard-Vessiot Theory
Connecting Galois theory to differential equations
Demonstrating field extensions and algebraic groups
Papers & Extended Articles
Participation in the UGS concludes with extended articles on the chosen topics.
