September 9, 2025, 10:00 am Science Building (SE-43), room 215
Speaker: Nurdaulet Shynarbek, Mathematics Educational Program Coordinator (In-person)
Title: Novel Representations of log 2 Through Polynomial Continued Fractions FLYER
Abstract: This presentation explores new representations of the mathematical constant log 2 using polynomial continued fractions. Building on previous work in continued fraction theory, we investigate a conjecture by Zhu He which proposes a specific polynomial continued fraction for log 2. We will demonstrate the validity of this conjecture and introduce an infinite family of new polynomial continued fractions for log 2.
September 9, 2025, 11:00 am Science Building (SE-43), room 215
Speaker: Alibek Orynbassar, Senior Lecturer, Department of Pedagogy of Natural Sciences, SDU University
Title: Complete Classification of Quadratic Irrationals with Period Two FLYER
Abstract: This talk presents a full classification of quadratic irrationals whose continued fraction expansions have period length two. While it is known that the continued fraction of N is periodic, the distribution of period lengths is less understood. We establish precise conditions for the period-two case and illustrate the results with numerical examples.
Bio: Alibek Orynbassar is a Senior Lecturer in the Department of Pedagogy of Natural Sciences at SDU University in Kaskelen, Kazakhstan, a position he has held since July 2023. He is currently pursuing a PhD in Mathematics and Natural Sciences at SDU.
He earned both his Master’s (2017) and Bachelor’s (2014) degrees in Mathematics and Natural Sciences from SDU. From July 2022 to June 2023, he was a Visiting Scholar at Teachers College, Columbia University, where he expanded his expertise in mathematics education and research.
Prior to his current role, he served as Mathematics Program Coordinator in the Department of Education at SDU (2020–2022) and as Senior Lecturer (2017–2022). Earlier in his career, he taught mathematics in secondary schools (2013–2017), where he prepared students for mathematics Olympiads. He has also contributed as a jury member for regional school mathematics Olympiads and scientific project competitions (2018–2020).
September 2, 2025, 10:00 am Science Building (SE-43), room 215
Speaker: Hansraj Jangir, Ph.D. student, Florida Atlantic University
Title: A Quasi-polynomial time Quantum Algorithm for the Extrapolated Dihedral Coset Problem. FLYER
Abstract: The Learning With Errors (LWE) problem, introduced by Regev (STOC’05), is one of the fundamental problems in lattice-based cryptography, believed to be hard even for quantum adversaries. Regev (FOCS’02) showed that LWE reduces to the quantum Dihedral Coset Problem (DCP) and later, Brakerski et al. (PKC 2018) extended this to the more general Extrapolated Dihedral Coset Problem (EDCP). In this talk, we present a quasi-polynomial time quantum algorithm for solving EDCP over power-of-two moduli, using a quasi-polynomial number of samples. We stress that our algorithm does not affect the security of LWE with standard parameters, as the reduction from standard LWE to EDCP limits the number of samples to be polynomial.
Bio: Hansraj is a PhD student in the Department of Mathematics and Statistics at Florida Atlantic University, Boca Raton. Prior to starting his doctoral studies, he worked as a Junior Research Fellow at the Defense Research and Development Organization (DRDO), Delhi. His research interests include lattice based cryptography and quantum algorithms.
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