Institute of Applied Mathematics (IAM) is an interdisciplinary centre fostering various researches and teaching activities in mathematical sciences. In order to coordinate mathematics-based research as well as to undertake collaborative research with industry, IAM has established Colloquia (General Seminars), since its foundation in 2002, almost every Tuesdays in the afternoon. A colloquium at the institute usually lasts about 45 minutes.

The Colloquium provides an opportunity to build and strengthen relations between researches, practitioners, regulators from various fields and members, especially the students, of IAM. Here, at IAM with four specialised departments (Actuarial Sciences, Cryptography, Financial Mathematics, Scientific Computing) we are expecting valuable contribution and exchange of ideas from different scholars, lecturers and specialists.

General audience of the Colloquia at IAM consists of both graduate and undergraduate students, scholars and academics from various research fields, including the departments at IAM. As the audience is not homogeneous, invited speakers are advised to consider the following general principles of a colloquium talk at IAM:

  • Colloquium talks are given to general audience; however, such a colloquium talk at IAM might sometimes resemble a research seminar (only when it is necessary).
  • A (colloquium) talk is not a paper, it needs a special preparation (pre-prep and pre-planning) in order to involve and attract as many attendees as possible to the subject. This is crucial if the audience is not homogeneous (with backgrounds from different research areas).
  • Mathematics is an expressive and precise language we communicate; however, reading mathematics (on board or on slides) distracts and disengage the audience from the speaker! Similarly, long tables, long algorithms, crowded charts or diagrams might be difficult to read and comprehend by the audience. So, special care is needed when necessary.
  • Facilities might improve the style of the talk. At IAM, besides the (white) board and transparencies, a projector connected to a computer is available for the electronic versions of the presentations.


Schedule


Speaker:  Prof. Dr. Timothy O'Brien, Department of Mathematics and Statistics, Loyola University Chicago, USA

Invited by:  Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 01.06.2021, 16:30-17:30 ( 1 hour ahead of normal time )

Abstract: To be announced later 


Speaker:  Prof. Dr. Hansjoerg Albrecher, Department of Actuarial Science, University of Lausanne, Switzerland

Invited by:  Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 25.05.2021 - 15.30

Abstract: 


Speaker: Prof. Dr. Erhan Bayraktar, Department of Mathematics, University of Michigan, USA

Invited by:  Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 18.05.2021 - 15.30

Abstract: We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with random weights characterized by an underlying graphon. The limit is given by a graphon particle system consisting of independent but heterogeneous nonlinear diffusions whose probability distributions are fully coupled. A law of large numbers result is established as the system size increases and the underlying graphons converge. Under suitable additional assumptions, we show the exponential ergodicity for the system, establish the uniform in time law of large numbers, and introduce the uniform in time Euler approximation. The precise rate of convergence of the Euler approximation is provided. Based on joint works with Suman Chakraborty and Ruoyu Wu. 


Speaker:  Assoc. Prof. Dr. Özlem Çavuş, Department of Industrial Engineering, Bilkent University, Turkey

Invited by:  Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 04.05.2021 - 15.30

Abstract: In classical multi-armed bandit problem, the aim is to find a policy maximizing the expected total reward, implicitly assuming that the decision maker is risk-neutral. On the other hand, the decision makers are risk-averse in some real life applications. In this study, we design a new setting based on the concept of dynamic risk measures where the aim is to find a policy with the best risk-adjusted total discounted outcome. We provide a theoretical analysis of multi-armed bandit problem with respect to this novel setting, and propose a priority-index heuristic which gives risk-averse allocation indices having a structure similar to Gittins index. Although an optimal policy is shown not always to have index-based form, empirical results express the excellence of this heuristic and show that with risk-averse allocation indices we can achieve optimal or near-optimal interpretable policies. 


Speaker:  Prof. Dr. Martin Redmann, Department of Mathematics, Martin Luther University of Halle Wittenberg, Germany

Invited by:  Hamdullah Yücel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 27.04.2021 - 15.30

Abstract: In this talk, we give a brief introduction to stochastic differential  equations (SDEs) with links to important applications. Subsequently, we discuss scenarios in which large scale SDEs appear. Solving these equations is connected to a high computational effort which, e.g., makes Monte  Carlo methods expensive. Model order reduction (MOR) can be used to reduce the dimension of large-scale SDEs leading to a lower computational complexity. We sketch the idea of MOR for stochastic systems and present some recent theoretical and numerical results.


Speaker:  Daniele Boffi, Applied Mathematics and Computational Science, KAUST

Invited by:  Önder Türk

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 20.04.2021 - 15.30

Abstract: We discuss the finite element approximation of eigenvalue problems arising from elliptic partial differential equations. We present various examples of non-standard schemes, including mixed finite elements, approximation of operators related to the least-squares finite element method, parameter dependent formulations such as those produced by the virtual element method. Each example is studied theoretically; advantages and disadvantages of each approach are pointed out.


Speaker:  Ralf Korn, Technical University Kaiserslautern, Germany

Invited by:  A. Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 26.01.2021 - 15.30

Abstract: We consider an investment and consumption problem in the face of a once-in-a-life-time event that causes the stock market to crash. However, there is no probabilistic information on the occurrence and the height of the crash. We are faced with what is called Knightean uncertainty. Thus, traditional portfolio optimization approaches are not applicable.  The talk contains an introduction into standard portfolio optimization methods and into the worst-case  pproach. A so-called life time consumption problem will be solved and leads to an explicit solution that depends on the character of the investor and that allows for economic interpretations. 


Speaker: Doğan Tırtıroğlu, Department of Real Estate Management, Ryerson University

Invited by:  A. Sevtap Kestel

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode:  724032

Date/Time: 18.01.2021 - 16.30

Abstract: Joint work with Belma OZTURKKAL and Basak TANYERI We posit a new hypothesis on the pricing of IPOs and provide evidence on it from IPOs issued in Turkey between 1989 and September 2020. The hypothesis focuses on how a sudden and unexpected regime switch in macroeconomic conditions, from decades-long high uncertainty to relative stability, affects the pricing of IPOs. We expect that macroeconomic stability should nurture (i) more IPOs, (ii) a shorter time length between two IPOs, and (iii) stylized findings, established internationally in the literature, to be more dominant. We take our empirical measure of macroeconomic fluctuations from the foreign exchange market. The February 2001 financial meltdown in Turkey is the switch event. The return generating process carries strongly the imprints of this meltdown, but not the other meltdowns witnessed during the sample period. Results from the *stability* ( *uncertainty*) regime are consistent with (differ starkly from) those reported for the developed economies, respectively. Remarkably and unexpectedly, high uncertainty "bleaches" even the well-established hot market effects on IPO initial-day returns. These are brand-new results in the literature and push macroeconomic uncertainty as a risk factor for IPOs to the forefront. Structural reforms to fend off the economic decay from the 2001 financial meltdown, including instituting a corporate debt market, have led to macroeconomic stability in Turkey. With that, the pricing of IPOs has become remarkably consistent with the well-established and stylized evidence from the developed economies. This paper also offers some preliminary work on a recent legal change with the aim to curb moral hazard in the IPO market in Turkey. Overall, Turkish issuers have left much less money on the table than others in the USA and elsewhere. This is another remarkable piece of finding and an addition to the rich list of puzzles of the IPO literature.


Speaker: Ramon Codina, Department of Civil and Environmental Engineering, Universitat Politècnica de Catalunya (UPC)

Invited by:  Önder Türk

Place: https://zoom.us/j/98408006920?pwd=eHQ2YzNMakxFamhDL1k1eDRTTURIQT09

Zoom Meeting ID: 984 0800 6920

Passcode: 724032

Date/Time: 12.01.2021 - 15.30

Abstract: When approximating numerically a mathematical model one often faces the need for many solves. This happens for example in optimisation, or when solutions need to be given depending on a parameter. In these situations, fine approximations are not affordable for all cases, but perhaps just a few, and coarse approximations need to be employed in most simulations. The idea of the methodology to be presented is to improve coarse solutions from the knowledge of fine solutions. This is in general convenient, and in some cases even necessary. Examples of the latter are those in which the coarse solution is unstable, or fails to satisfy basic physical principles (for example, equilibrium). What we propose in this talk is to introduce a correction of the coarse model, depending on the coarse solution, designed to obtain a coarse solution as close as possible to the (projection of the) fine solution for the situations (that we call configurations) in which the fine solution is known. This corrective term is designed using an Artificial Neural Network, having as training set the collection of fine solutions for the configurations in which these are available. We have applied this concept to different problems: a) In Reduced Order Modelling (ROM), where the coarse model is built from a reduced basis and the training set are the collection of snapshots of departure, b) In the coarsening of finite element meshes in space, in which a fine solution is known in a fine mesh but then this mesh is coarsened to continue the simulation, c) In increasing the time step size in transient problem, in particular in wave propagation. Nevertheless, many other applications can be devised for the general concept proposed.