A Panorama of Geometry (2023)

Convener(s)

Name: Prof. Amritanshu Prasad Dr. Sushmita Venugopalan
Mailing Address:  The Institute of Mathematical Sciences, Chennai 600113  The Institute of Mathematical Sciences, Chennai 600113
Email:  amri at imsc.res.in  sushmita at imsc.res.in

The goal of this workshop is to introduce participants to different ways of studying geometric spaces. Besides introducing the differential, algebraic, and computational approaches, the workshop also includes an activity-based course where various geometric results are proved in a visual or tactile way. We will aim to have overlaps between the courses to emphasize how the same spaces can be studied from different points of view.

Dates: 

Monday, November 20, 2023 - 19:00 to Saturday, November 25, 2023 - 19:00

Venue: 

Venue Address: 

The Institute of Mathematical Sciences, CIT campus, Taramani Chennai 600113

 

 

Venue State: 

Venue City: 

PIN: 

600113

Syllabus: 

 

Name of the Speaker with affiliation

No. of Lecture s

Detailed Syllabus

Sushmita Venugopalan (SV) Reader, IMSc, Chennai

9 hours

 Title :  An introduction to algebraic geometry
Syllabus :
* Affine varieties, Zariski topology, Hilbert's Nullstellensatz, Projective space, Projective varieties.
* Examples : Conics and Cubics, Twisted cubic, Veronese and Segre maps.
* Grassmanians.
* Dimension and degree.
* Blowing up points.

Vijay Ravikumar (VR)
Azim Premji University, Bengaluru

9 hours

 Title : Discovering geometry through our physical senses

Part 1 : Geometry of vision
* From perspective drawing to RP2 as the extended Euclidean plane.
* Projective geometry: Duality; Desargues' Theorem, Pappus's Theorem.
* Fundamental Theorem of Projective Geometry.
* Cross ratio : an invariant of perspective change.
* Three point perspective, RP3 as the extended euclidean space.

Part 2 : Topology of movement
* SO(3) as the set of spatial rotations.
* Topology of SO(3) via a series of movement challenges.
* Quaternion representation of spatial rotations.
* Proof that SO(3) = RP3.
* Time permitting : Hopf fibration.

Parameshwaran Sankaran (PS) Professor,

CMI, Chennai

4.5

hours

  Title: Geometry of the Poincaré upper half plane.
*  Surfaces in R^3.
* Arc length--geodesics.  Examples--spheres, torus. Riemannian metric. Poincaré upper half space H.
* Isometry groups of S^2,R^2, and H. Properties of (geodesic) triangles.  Area formula.
* Notion of curvature (for surfaces)--examples. Euler characteristics, Gauss-Bonnet formula.
* Generalization to higher dimensions, if time permits.

Amritanshu Prasad (AP) Professor, IMSc, Chennai

4.5

hours

 Title : Groebner bases
*Monomial orders, division algorithm for multivariate
polynomials.
* Dickson's lemma and Hilbert basis theorem
using Groebner bases.
* Properties of Groebner bases.

 

 

References:

 

  1.  Algebraic Geometry by Joe Harris.

  2. An invitation to algebraic geometry by Karen E. Smith , Lauri Kahanpää , Pekka Kekäläinen , William Traves. 

  3.  The Four Pillars of Geometry by John Stillwell.

  4. Perspective and Projective Geometry by Annalisa Crannell, Fumiko Futamura, and Marc Frantz.

  5.  Projective Geometry by HSM Coxeter

  6.  Naive Lie Theory by John Stillwell

  7. Lecture Notes on Elementary Topology and Geometry (Springer UTM) by  I. M. Singer and J A Thorpe.

  8. Hyperbolic Geometry by A F Beardon.

  9. Ideals, Varieties, and Algorithms (Springer UTM) by Cox, Little and O'Shea.

 

 

Name of the tutors

S. No.

Name

Affiliation

1

Abhirup Chatterjee (AC)

IMSc

2

S Velmurugan (VM)

IMSc

3

Manika Gupta (MG)

IMSc

Time Table: 

 

Day

Date

Lecture 1

9:30–11:00

Tea 11.00
to
11:30

Lecturer 2

11.30–1.00

Lunch
1.00
to
2.00

Lecture 4

2.00-3.30

Tea 3.35
to
3.55

Discussion 4.00-5.00

Snacks 5.05
to

5.30

 

 

(Speaker’s name)

 

(Speaker’s name)

 

(Speaker’s name)

 

(Tutor’s name)

 

Mon

20

SV

 

VR

 

PS

 

SV+AC+MG

 

Tue

21

SV

 

VR

 

PS

 

VR+AC+VM

 

Wed

22

SV

 

VR

 

PS

 

PS+VM+MG

 

Thu

23

SV

 

VR

 

AP

 

SV+AC+MG

 

Fri

24

SV

 

VR

 

AP

 

VR+AC+VM

 

Sat

25

SV

 

VR

 

AP

 

AP+VM+MG

 

Selected Applicants: 

 Note:- Accommodation will not be provided. Participants have to arrange their own accommodation

sr.n SID Full Name Gender Affiliation Position In College/ University University/Institute M.Sc./M.A. Year Of Passing M.Sc./M.A Ph.D. Degree Date
1 50526 Mr. Rounak Majumdar Male Na Na University Of Hyderabad 2022  
2 50527 Mrs Sofi A Francis Female Dr.Ngp Arts And Science College,Coimbatore Ph.D Scholar Calicut University 2010  
3 50568 Mr Balaji . E Male Nehru School Of Architecture Associate Professor Of Mathematics E Rode Arts And Science College, Bharathiyar University 2006  
4 50574 Mr Nitesh Sharma Male Iiitd Phd Student South Asian University 2020  
5 50577 Mr. Ayan Dutta Male Indian Association For The Cultivation Of Science Msc Student Indian Association For The Cultivation Of Science M.Sc. Awaiting Result  
6 50579 Mr. Mahesh Krishna K Male Isi Bangalore Postdoc Mangalore University 2014 17/02/2022
7 50586 Mr. Supriyo Jana Male Iit Madras Phd Iit Madras 2021  
8 50615 Ms Tanushree L Female Avinashilingam University Msc Student M.Sc Awaiting Result  
9 50622 Dr Krishna Kishore Male Indian Institute Of Technology Tirupati Assistant Professor Indiana University Bloomington 2010 20/12/2014
10 50676 Mr. Tikam Chand Soyal Male Hada Rani Govt. Pg College Salumber Asst. Prof. Iit Gandhinagar 2018  
11 50742 Mr Hasan Shaikh Male Aligarh Muslim University M.Tech Student Aligarh Muslim University Awaiting Result  
12 50749 Mr. Ritabrata Bhattacharyya Male Chennai Mathematical Institute Bsc 3rd Year      
13 50753 Mr. Bidhan Paul Male Iit Madras Phd Student Iit Madras 2019  
14 50799 Dr. Kamlesh Kumar Dubey Male Invertis University, Bareilly, Up India Assoc. Prof. M Sc From University Of Allahabad 2002 26/08/2006
15 50833 Mr Md Hifzur Rahaman Male Aligarh Muslim University Phd Aligarh Muslim University 2020  
16 50849 Mr. Mohd Junaid Male Aligarh Muslim University Ph.D. Aligarh Muslim University 2020 02/06/2022
17 50898 Mr. Indrashis Gain Male Indian Institute Of Technology Palakkad Msc Student Indian Institute Of Technology Palakkad Awaiting Result  
18 51007 Mr Ramveer Singh Male Indian Institute Of Science Education And Research Phd Iiser Tirupati 2021  
19 51015 Mr. Sashadhar Dutta Male Ramakrishna Mission Vivekananda Centenary College, Rahara Msc Student Ramakrishna Mission Vivekananda Centenary College    
20 51021 Mr. Vinay Kumar Male University Of Lucknow Ph.D. Scholar Bba University Lucknow 2016  
21 51042 Mr. Samiran Nayek Male Indian Institute Of Technology, Tirupati Research Scholar Indian Institute Of Technology, Tirupati 2022  
22 51071 Dr, Dr Rajeev Prakash Shrivastava Male Www.Rajeev-Shrivastava.Com Na Bhopal University Bhopal 1987 17/03/2000
23 51073 Dr. Punam Gupta Female Dr. Harisingh Gour Vishwavidyalaya (A Central University) Assistant Professor Banaras Hindu University 2007 25/01/2011
24 51109 Ms. Pooja Gupta Female University Of Lucknow Phd (Research Scholar) M.Sc. From University Of Lucknow 2017  
25 51125 Mr. Abhisek Kar Male Indian Institute Of Science Education And Research Pune Teaching Assistant And Project Student Indian Institute Of Science Education And Research Kolkata Awaiting Result  
26 51126 Mr. Karunagaran K Male Anna University Teaching Fellow University Of Madras    
27 51169 Mr. Ram Shankar Chaudhary Male Banaras Hindu University Phd Student Motilal Nehru National Institute Of Technology, Allahabad 2018  
28 51173 Mr. Arun Kumar Bhardwaj Male University Of Lucknow Research Scholar M.Sc. 2013  
29 51207 Mr. Abhinav Verma Male University Of Lucknow Phd (Scholar) University Of Lucknow 2020  
30 51217 Mr. Vindhyachal Singh Yadav Male University Of Lucknow Phd (Scholar) University Of Allahabad 1981  
31 51238 Mr. Sayan Sahajad Gazi Male Maulana Abul Kalam Azad University Of Technology Msc Student Maulana Abul Kalam Azad University Of Technology Awaiting Result  
32 51327 Mr Nikhil Purushottam Zade Male Visvesvaraya National Institute Of Technology Phd Visvesvaraya National Institute Of Technology 2020  
33 51351 Dr. Lalit Vaishya Male The Institute Of Mathematical Sciences, Chennai Post Doctoral Fellow Banaras Hindu University Varanasi India 2014 13/08/2021
34 51395 Ms. Sayana Mohammed Salooj Female St Berchmans College Predoctoral Fellow St Berchmans College, Changanasserry, Kerala Awaiting Result  
35 51396 Mr. Tamoghna Kar Male Indian Institute Of Technology Palakkad Junior Research Fellow Ramakrishna Mission Vivekananda Educational And Research Institute (Rkmveri) 2022  
36 51542 Mr. Thyagarajan M Male Agurchand Manmull Jain College Asst. Prof. Anna University 2005  
37 51550 Mr Murugan M Male Agurchand Manmull Jain College Assistant Professor University Of Madras 2012  
38 51577 Mr. Tarun Saxena Male Banaras Hindu University Phd Student University Of Allahabad 2020  
39 51618 Ms Shruti Priya Female Indian Institute Of Technology, Kharagpur Phd Nit Rourkela 2020  
40 51635 Dr. Mehraj Ahmad Lone Male National Institute Of Technology Srinagar, J&K Assistant Profesoor Jamia Millia Islamia 2012 17/11/2017
41 51700 Mr. Sourajyoti Maiti Male Ramakrishna Mission Vivekananda Educational And Research Institute (Passed M.Sc In 2023) M.Sc Graduate Ramakrishna Mission Vivekananda Educational And Research Institute Awaiting Result  
42 51723 Ms. Jaspreet Kaur Female Central University Of Punjab Phd (Research Scholar) Punjabi University, Patiala 2016  
43 51726 Ms. Jyoti Yadav Female Central University Of Punjab Phd University Of Rajasthan 2018  
44 51727 Ms. Seema Jangir Female Central University Of Punjab Phd Student University Of Delhi 2018  
45 51738 Ms. Adeeba Zaidi Female Central University Of Punjab Phd Scholar D. B. S. Pg College, Hemvati Nandan Bahuguna Garhwal University Uttarakhand 2017  
46 51751 Mr. Shayon Bhadra Male Bits Pilani Hyderabad Campus Phd Student Tezpur University 2019  
47 51923 Mr. Mifron Fernandes Male Iit Madras Passed Out Msc Student Iit Madras 2022  
48 51953 Mr. Aman Singh Male Iiser Mohali Phd Kerala School Of Mathematics 2022  
49 52009 Mr Gnanam Mahesh Kalakaoi Male Agurchand Manmull Jain College Assistant Professor Loyola College 2013  
50 52021 Mr. Paramhans Kushwaha Male Iit Jammu Phd Iit Delhi 2020  
51 52171 Ms Rachna Aggarwal Female Iiser Mohali Post Doctoral Fellow University Of Delhi 2011  
52 52237 Ms. Shivani Goel Female Indraprastha Institute Of Information Technology, Delhi Phd Chaudhary Charan Singh University, Meerut 2018  
53 52321 Ms. Dishari Bhaduri Female Madras Christian College Research Student      
54 52405 Mr Swapnil Deepak Malegaonkar Male Srm University Ap Phd Student Hyderabad Central University 2015  
55 52426 Mr. Sivasankar R Male Indian Institute Of Technology Tirupati Ph.D Scholar Manonmaniam Sundaranar University, Tirunelveli 2020  
56 52757 Mr. Somnath Mondal Male Iitm Phd Banaras Hindu University 2021  
57 52761 Mr. Elanchearan R S Male Indian Institute Of Technology Madras Phd Indian Institute Of Technology Madras 2020  
58 52859 Mr. Subhranil Deb Male Chennai Mathematical Institute Bsc Student      
59 52872 Mr. Nirmal Kumar N Male College Of Engineering Guindy Msc Student College Of Engineering Guindy 2022  
60 52879 Mr. Souvik Mandal Male Iit Madras Phd Student Indian Statistical Institute, Bangalore Centre 2021  
61 52974 Mr Arun Ruthraa Male St Joseph's University Bengaluru Msc Student St Joseph's University Bengaluru 2022  
62 53002 Mr Rigen Tamang Male Indian Institute Of Technology (Bhu) Varanasi Phd Indian Institute Of Technology Kharagpur 2020  
63 53037 Dr Baby Smitha K.M Female Devaswom Board College Assistant Professor M.Sc 2004 03/09/2019
64 53058 Ms Adithi Iyer Female Iit Gandhinagar Phd Nagpur University 2018  
65 53111 Ms. Vijaya Dharshini T Female Sri G. V. G. Visalakshi College For Women M. Sc Student Sri Gvg Visalakshi College For Women    
66 53125 Mr Naman Kumawat Male Central University Of Rajasthan Msc-Bed Student Central University Of Rajasthan Awaiting Result  
67 53132 Mr. Deepak Joy Male Iit Madras Phd Central University Of Kerala 2021  
68 53138 Ms. Akila Visali R Female Sri Gvg Visalakshi College For Women Student      
69 53139 Ms. Charukeshini Saravanakumar Female Sri G.V.G. Visalakshi College For Women Msc Student Sri G.V.G. Visalakshi College For Women    
70 53185 Ms Samraggi Ghosh Female Iit Mandi Researcher Rāiganj University 2017  
71 53199 Ms. Gnanadharshini N Female Sri G.V.G. Visalakshi College For Women Msc Student Sri G.V.G. Visalakshi College For Women    
72 53241 Dr. Tejbir Lohan Male The Institute Of Mathematical Sciences Chennai Visiting Position Iit Kanpur 2018 05/09/2023
73 53319 Ms. Neha Garg Female Indian Institute Of Technology, Gandhinagar Project Associate Panjab University 2016  
74 53320 Mrs Franklin Thamil Selvi Female Sathyabama Institute Of Science And Technology Assistant Professor Loyola College 2004  
75 53329 Mr. Yuvaraj A Male Thiruvalluvar University Phd Thiruvalluvar University, Serkkadu, Vellore -632115. Tamil Nadu, India. Awaiting Result  
76 53337 Mrs Mary Metilda M.I Female Sathyabama Institute Of Science And Technology Assistant Professor Sacred Heart College, Thirupathur 2005  
77 53376 Ms Sindhoora M R Female Manipal Institution Of Technology, Manipal Msc Student Manipal Academy Of Higher Education, Manipal    
78 53412 Mrs Neelam Kanwar Female Central University Of Rajasthan Int Msc Bed Student Central University Of Rajasthan Awaiting Result  
79 53432 Dr. Prashant Tiwari Male Hri Prayagraj Post Doctoral Fellow M.S. 2018 03/07/2022
80 53456 Mr. Susobhan Mazumdar Male St. Joseph's University, Bangalore Assistant Professor Indian Institute Of Technology, Madras/ Indian Institute Of Technology/ M.Sc 2010  

 

How to Reach: 

TBA

School Short Name: 

apg

Last Date Application: 

Monday, August 15, 2022

School Type: 

TEW

Separate faculty form: 

0