IASBS Mathematics Colloquium

Autumn 1396

1396-07-04
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1396-07-11
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1396-07-18
Speaker: Ali Dadkhah (Ferdowsi University of Mashhad)
Title:
بررسي و تعميم برخي از نامساوي هاي مهم در نظريه اطلاعات كوانتومي
Abstract:
رابطه نزديكي بين فضاهاي هيلبرت كه فضاهاي برداري خاصي همراه با يك ضرب داخلي مي‌باشند و فضاهاي حالات يك سيستم كوانتومي وجود دارد به عنوان مثال يكي از فضاهاي هيلبرت مهم و شناخته شده كه در مكانيك كوانتومي كاربرد زيادي دارد فضاي ماتريس هاي مربعي با درايه ها در اعداد مختلط مي‌باشد. در اين سخنراني سعي داريم به طور ساده اين رابطه را بيان و با ارايه مثالهايي به توصيف آن بپردازيم. در ادامه بعضي از نامساوي هاي مهم در مكانيك كوانتوم مانند اصل عدم قطعيت هايزنبرگ را بيان و تعميم هايي از آن ها را ارايه مي‌كنيم.
References:
1. A. Dadkhah and M.S. Moslehian, Quantum information inequalities via tracial positive linear maps, J. Math. Anal. Appl. 447(1) (2017), 666-680.
2. G. Toth and D. Petz, Extremal properties of the variance and the quantum Fisher information, Phys. Rev. A 87 032324 (2013).
3. K. Yanagi, S. Furuichi, and K. Kuriyama, A generalized skew information and uncertainty relation, IEEE Trans. Inform. Theory 51 (2005), 4401ā€“4404.

1396-07-25
Speaker: (Cancelled)
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1396-08-02
Speaker: Fazlollah Soleymani (IASBS)
Title: On the construction of an efficient scheme for outer generalized inverses with applications
Abstract: We discuss a hyperpower iteration for numerical computation of the outer generalized inverse of a matrix. The constructed scheme yields a high efficiency index. Error analysis and a stabilized form of the scheme are also discussed. Some applications in financial mathematics and numerical linear algebra are pointed out as well.

1396-08-09
Speaker: Mohammad Farrokhi Derakhshandeh Ghouchan (IASBS)
Title: Lattice paths inside a table
Abstract: We consider a class of lattice paths defined in an $m\times n$ table beginning from the first column and ending at the last column. Writing the number of paths from the first column to a given cell into that cell makes every row and column of the table into a numerical vector. We distinguish relations between rows and columns, respectively, which enable us to count the number of such paths.

1396-08-16 (Special Talk)
Speaker: AmirHosein Sadeghimanesh (University of Copenhagen, Denmark)
Title: Mathematics of chemical reaction networks
Abstract: In this talk we introduce chemical reaction networks and associate a graph and a dynamical system with them. Then we replace the dynamical system with a polynomial ideal which is enough for studying many of interesting properties of the network. The most important property among these is Multistationarity. We discuss this property and mention some of its applications. Finally we mention three famous questions and what we have done for them briefly without proofs. The goal of this lecture is just to introduce this field of study and some of its beauties.

1396-08-16
Speaker: Vahid Ghorbani (Urmia University)
Title: Introduction to matroid theory
Abstract: Hassler Whitney introduced the theory of matroids in 1935 and developed a striking number of their basic properties as well as different ways to formulate the notion of a matroid. Examples of matroids arise from graphs, matrices, configurations of points, arrangements of hyperplanes, and geometric lattices; matroids play an essential role in combinatorial optimization. In this talk, I will introduce some notation and outlines some basic concepts of matroid theory and I will present some classes of matroids such as $F$-representable, graphic, cographic, transversal, algebraic and regular matroid. This talk will review some of the exciting recent work in matroid theory at Urmia university that is inspired by the graph operations.
Contents:
1. General definition of matroids
2. Equivalent definition
3. Introduction of some well-known classes of matroids
4. Duality and minor
5. Excluded minors summary
6. Matroid connectivity
7. Application of matroids in graph theory
8. Extension operations fram graphs to matroids

1396-08-23
Speaker: Amir Amiraslani (University of Hawaii Maui College, USA)
Title: $LU$ factors for linearization of matrix polynomials
Abstract: In this talk, we consider a regular matrix polynomial $P(\lambda)=\sum_{j=0}^nA_jf_j(\lambda)$ of degree $n$ where $A_j$ are $s\times s$ complex matrices and $f_j(\lambda)$ are the basis elements. We first see how to linearize this matrix polynomial to arrive at a matrix pencil of the form $\lambda C_1-C_0$. We then find the structured $LU$ factors of this pencil which can be used in root-finding algorithms among other applications. Various polynomial bases are considered and discussed.

1396-08-30
Speaker: Ali Taherkhani (IASBS)
Title: Chromatic number of categorical product of hypergraphs
Abstract: More than 50 years ago Hedetniemi conjectured that the chromatic number of categorical product of two graphs is equal to the minimum of the chromatic numbers of the factors. This conjecture has received a considerable attention in recent years. Hedetniemiā€™s conjecture was generalized to hypergraphs by Zhu in 1992. In this talk first we will present a review of some recent results surrounding Hedetniemiā€™s conjecture. Then, by using a topological method, we show that a new lower bound for the chromatic number of categorical product of general Kneser hypergraphs. Using this lower bound, we enrich the family of hypergraphs satisfying Zhuā€™s conjecture.

1396-09-07
Speaker: (Cancelled)
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1396-09-14
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1396-09-21
Speaker: (Cancelled)
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1396-09-28
Speaker: (Cancelled)
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