Course Name: Probabilistic Methods in PDE

Course abstract

Probabilistic method in PDE is equally used in Pure and Applied Mathematics research. This is regarded as a very powerful tool by the researchers working on the theory of differential equations. However, as the topic demands expertise on both PDE and probability theory, an initiative to teach the topic as a structured course is vastly absent globally, including in India. There is hardly any lecture note or a course accessible for the mathematics students. There is no book for mathematics students which focuses on this topic and assembles all important aspects suitable for an introduction to this topic. Young researchers like PhD students or junior postdoctoral fellows, who aspire to learn the topic, resorts on several different books and study by themselves, which often consumes considerable amount of their productive time. To change the present discouraging scenario and to boost up research on this very powerful and vibrant topic, I have designed this introductory course. I have offered this once informally at IISER Pune and then officially at Justus-Liebig University, Giessen, Germany for research students. This course, although an advanced one, attracts students with a background of PDE, Probability Theory, Mathematical Finance, or Mathematical Physics. This course allows a researcher to confidently take up an original research problem in the related field. This course content is mainly based on two different books, one on stochastic calculus and another on semigroup theory. Many theorems would be proved in the lectures with greater details than the reference books.


Course Instructor

Media Object

Prof. Anindya Goswami

Dr. Anindya Goswami received his Bachelor's degree in Mathematics from St. Xavier's College, Calcutta in 2002. Later in the same year, he joined the Integrated Ph.D. program in the Department of Mathematics in Indian Institute of Science, Bangalore. Following the completion of his MS degree in 2005, He received the SPM fellowship as part of the National Award for best performance in National Eligibility Test in Mathematical Sciences. His MS thesis was titled “Controlled Semi-Markov Processes with Partial Observation”. He was bestowed with the Doctorate degree from the Department of Mathematics, IISc in the year 2008. (Link to my Ph.D thesis-“Semi-Markov Processes in Dynamic Games and Finance”) The following three years, I carried out my postdoctoral research in the University of Twente, Netherlands; INRIA- Rennes, France; and Technion- Israel Institute of Technology, Israel respectively. He joined IISER Pune as an Assistant Professor in fall, 2011. Since then, He have offered a variety of graduate and undergraduate courses- Multivariable Calculus, Point-set Topology, Measure Theory, Functional Analysis, Numerical Analysis, Stochastic Processes, Mathematical Finance, to name a few. I am reappointed at the same department as an Associate Professor in spring, 2018. My current research interest comprises of Non-cooperative Stochastic Dynamic Game, Stochastic Control, Mathematical Finance, and Queueing Network. So far, I have coauthored many peer-reviewed research articles published in well-reputed journals including J. Math. Anal. Appl., SIAM J. Control Optim., Appl. Math. Optim., Electron. Commun. Probab., Statist. Probab. Lett. and Stoch. Anal. Appl. I am an invited reviewer of Mathematical Reviews, published by American Mathematical Society and He also regularly take up refereeing responsibility from several Mathematics journals and book publishers.
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Teaching Assistant(s)

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 Course Duration : Jan-Apr 2021

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 Syllabus

 Enrollment : 18-Nov-2020 to 25-Jan-2021

 Exam registration : 15-Jan-2021 to 12-Mar-2021

 Exam Date : 25-Apr-2021

Enrolled

269

Registered

2

Certificate Eligible

Will be announced

Certified Category Count

Gold

0

Silver

0

Elite

0

Successfully completed

0

Participation

0

Success

Elite

Silver

Gold





Legend

AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75 AND FINAL SCORE >=40
BASED ON THE FINAL SCORE, Certificate criteria will be as below:
>=90 - Elite + Gold
75-89 -Elite + Silver
>=60 - Elite
40-59 - Successfully Completed

Final Score Calculation Logic

  • Assignment Score = Average of best 8 out of 12 assignments.
  • Final Score(Score on Certificate)= 75% of Exam Score + 25% of Assignment Score
Note:
We have taken best assignment score from both Jan 2020 and Jan2021 course
Probabilistic Methods in PDE - Toppers list

Enrollment Statistics

Total Enrollment: 269

Registration Statistics

Total Registration : 2

Assignment Statistics




Assignment

Exam score

Final score

Score Distribution Graph - Legend

Assignment Score: Distribution of average scores garnered by students per assignment.
Exam Score : Distribution of the final exam score of students.
Final Score : Distribution of the combined score of assignments and final exam, based on the score logic.