INSTITUTE SEMINAR DAYS

April 9 and 16, 2018

Venue: Ramanujan Auditorium, IMSc

(Scroll down for April 9 schedule and abstracts)

SCHEDULE April 16, 2018

Speaker | Title | |

10:00 | KA Chandrashekar | French Flag Model of Cellular differentiation |

10:15 | Avijit Nath | Cobordism of generalized Dold manifolds |

10:30 | Abhisekh Sankaran | Logical fractals |

10:45 | B. S. Karthikeyan | Compilation, curation and exploration of the phytochemical space of Indian medicinal plants |

11:00 | Ria Ghosh | Emergent complexity of biologically excitable-passive cell motifs |

11:15 | Anantha Padmanabha | How to play when you are not sure? |

11:30 | Coffee break | |

12:00 | Hans van Ditmarsch | Distributed Dynamic Epistemic Logic |

12:15 | Vani Vemparala | Like-charged polymers like themselves |

12:30 | Vibha Sahlot | Conflicts in geometry |

12:45 | R. Rajesh | Does shaking imitate a temperature bath? |

13:00 | Lunch | |

14:30 | Diptapriyo Majumdar | Algorithms that exploit some Structure of the Input |

14:45 | Arpan Kundu | Conserved charges in gravity |

15:00 | Mukul Laad | Non-BCS superconductivity in Bismuth |

15:15 | Arijit Ghosh | Polynomial Partitioning Lemma and its Applications in Combinatorial Geometry |

15:30 | Coffee break | |

16:00 | Vigneshwar N | Entropy Driven Transitions - A system of hard rods |

16:15 | R. Ganesh | In how many ways can four vectors add to zero? |

16:30 | Md Izhar Ashraf | The handedness of language |

16:45 | Rahul Siddharthan | Finding frequent misspelled words in a text |

KA Chandrashekar

Title: French Flag Model of Cellular differentiation

Abstract: The central problem in developmental biology is to understand the processes by which a single cell (zygote) gives rise to a multicellular organism with various specialized cells in a very robust extremely reproducible way. French Flag Model proposed by Lewis Wolpert in 1969 is one of the simplest yet ubiquitous mechanism through which identical cells are made to achieve different cell fates by creating spatial heterogeneity, often through a morphogen gradient.

Avijit Nath

Title: Cobordism of generalized Dold manifolds.

Abstract: I will introduce the notion of Cobordism and cobordism of

generalized Dold manifolds.

Abhisekh Sankaran

Title: Logical fractals

Abstract: Fractals are mathematical objects that exhibit self-similarity at all scales, for a suitable notion of scale and a precise notion of similarity that is usually based on isomorphism. We consider a notion of similarity based on logic, and consider the corresponding fractal property. Classes of structures satisfying this property are called *logical fractals*. We show that such fractals are ubiquitous in computer science. We further show that for most of these fractals, there exist fixed parameter tractable (FPT) algorithms that produce for any given structure, a logically self-similar structure at any given scale, in linear time.

B. S. Karthikeyan

Title: Compilation, curation and exploration of the phytochemical space of Indian medicinal plants

Abstract: Phytochemical constituents of medicinal plants encompass a diverse chemical space for drug discovery. India is rich with a flora of indigenous medicinal plants that have been used for centuries in traditional Indian medicine to treat human maladies. A comprehensive online resource on the phytochemistry of Indian medicinal plants will enable computational approaches towards natural product-based drug discovery. In this talk, I will present, IMPPAT, the most- comprehensive, freely available, curated, digital database of 1742 Indian Medicinal Plants, 9596 Phytochemicals, And 1124 Therapeutic uses spanning 27074 plant-phytochemical associations and 11514 plant-therapeutic associations. Notably, our curation effort led to a non-redundant in silico library of 9596 phytochemicals with standard chemical identifiers and structure information. Using cheminformatic approaches, we have computed the physicochemical, ADMET and drug-likeliness properties of the IMPPAT phytochemicals. We show that the structural complexity of IMPPAT phytochemicals differ from libraries of commercial compounds or diversity-oriented synthesis compounds while being similar to other libraries of natural products. Within IMPPAT, we have filtered a subset of 960 potential druggable phytochemicals, of which majority have no significant similarity to existing FDA approved drugs, and thus, rendering them as good candidates for prospective drugs. IMPPAT is accessible at: https://cb.imsc.res.in/imppat

Ria Ghosh

Title: Emergent complexity of biologically excitable-passive cell motifs

Abstract: Electrically coupled excitable and passive cells are ubiquitous in biological tissues. Here, we systematically investigate the emergent dynamics in networks consisting of these two cell types in order to unravel the complexity of the dynamical activity observed in such systems. Though simple in topology, these systems exhibit a rich variety of different dynamical regimes including the existence of chaos.

Anantha Padmanabha

Title: How to play when you are not sure?

Abstract: Games with imperfect information is the setting where players have only partial information about the game itself or the other players' moves. For instance if you just know that the opponent has made some move but you don't know which particular move it is. How should you respond? In this talk we shall discuss what it means to have partial information in a game using some examples and see how to use logic to reason about games in such settings.

Hans van Ditmarsch (UMI/Relax CNRS professor at imsc)

Title: Distributed Dynamic Epistemic Logic

Abstract: In dynamic epistemic logic messages are typically (i) correct, (ii) instantaneously sent and received, and (iii) coming from an outside source. In distributed computing the more general setting is common wherein (i) messages may be incorrect and even intentionally so, (ii) are received after they have been sent or are not received at all, and (iii) sent between agents or processes. We present attempts at integration of dynamic epistemic logic and distributed computing.

Vani Vemparala

Title: Like-charged polymers like themselves

Abstract:

Physics and Paula Abdul say 'opposites attract' but similar also like each other, as a matter of fact. Same-charged polymers can compactify and aggregate, maybe sounds counter-intuitive? I will try & validate.

Vibha Sahlot

Title: Conflicts in geometry

Abstract: The talk is motivated by choice problems in computer science literature. In these problems there are conflicts on the objects in some underlying problem such that it precludes some objects from being part of the solution if some others are in the solution.

Consider the Wireless Antenna Coverage problem. In this problem, we need to place a minimum number of wireless antennas (servers) at some predefined locations in order to service a group of clients. We model this problem as Discrete Unit Disk Cover (after some simplifications). Here, we are given a set of points that correspond to clients, and a set of unit disks in the plane corresponding to servers. We need to choose a minimum number of disks from the given input into the solution, such that all clients are covered. In view of the adverse effect of radio waves in case of mobile tower aloocation, it might not be wise to place two towers in close proximity. That is, the placement of a tower at one place restrains us to place towers in all nearby locations. To model this, we need to incorporate these constraints in our previous model. We call these restrictions as conflicts. Here, two servers are in conflict when at most one of them can be chosen to be in the solution.

In this talk we shall discuss the computational aspects of such problems.

R. Rajesh

Title: Does shaking imitate a temperature bath?

Abstract: The velocity distribution of a gas in equilibrium is well-known to be Maxwellian (Gaussian). What is the velocity distribution for a collection of inelastic particles that is driven to a steady state through continuous injection of energy? This is the central question in the kinetic theory for dilute inelastic gases — which is widely used in developing phenomenological models for driven granular systems. In this talk, I will summarize some of our recent work on this topic.

Diptapriyo Majumdar

Title: Algorithms that exploit some Structure of the Input

Abstract: Most of the real world problems are computationally hard and we do not expect efficient algorithms to solve them. But, if the solution size is small enough, then some of those problems can be solved efficiently. This is a classical approach for parameterization used in Parameterized Complexity. Alternately even if we do not know a bound on the solution size, sometimes the problem can be solved efficiently if the input has some structure which can be captured by a potentially small parameter. This is a recent trend in parameterized complexity. In this talk, we will discuss such algorithms for a few computational problems.

Arpan Kundu

Title: Conserved charges in gravity

Abstract: I shall start with the more familiar conservation laws in Physics like energy, momentum and angular momentum conservation. I shall argue that how these conservation laws follow from time translation, space translation, and rotation symmetry. Then I shall talk about the conserved charges in general relativity namely supertranslation charge and argue how they follow from supertranslation symmetry, which is a local generalization of the usual translation.

Mukul Laad

Title: Non-BCS superconductivity in Bismuth

Abstract: Motivated by the remarkable discovery of superconductivity in elemental Bismuth at ambient pressure, we study its normal state in detail using a combination of tight-binding (TB) band-structure supplemented by dynamical mean-field theory (DMFT). We show that a two-fluid model composed of preformed and dynamically fluctuating excitons coupled to a tiny number of carriers provides a unified rationalization of a range of ill-understood normal state spectral and transport data. Based on these, we propose that resonant scattering involving a very low density of renormalized carriers and the excitonic liquid drives logarithmic enhancement of vertex corrections, boosting superconductivity in Bi. A confirmatory test for our proposal would be the experimental verification of an excitonic semiconductor with electronic nematicity as a ‘competing order’ on inducing a semi-metal-to semiconductor transition in Bi by an external perturbation like pressure.

S. Koley, M. S. Laad and A. Tarahder, Scientific Reports 7, Art. #: 10993

(2017), doi:10.1038/s41598-017-11269-y

Arijit Ghosh

Title: Polynomial Partitioning Lemma and its Applications in Combinatorial Geometry

Abstract: I will introduce Guth-Katz's Polynomial Partitioning Lemma and show some applications of the lemma in Combinatorial Geometry.

Vigneshwar N

Title: Entropy Driven Transitions - A system of hard rods

Abstract: I will start with a brief introduction of entropy driven transitions and contrast it with energetically driven transitions and also offer some historical perspectives and experimental examples. I will also talk about the toy model of hard rods in both 2D and 3D of length k, interacting only via hard core repulsion on a square and cubic lattices. This model will also serve as a pedagogical tool to introduce lattice gas models of hard particles. In this, we show what types of orderings are possible and how the phase diagram changes as a function of k and how a simple system with no attractive potentials can have an ordered phase.

R. Ganesh

Title: In how many ways can four vectors add to zero?

Abstract: A common motif in magnetism is a unit of four spins that live on the corners of a tetrahedron. To lower energy, these spins must add to zero. I will discuss how this maps to a particle living in a five dimensional space, but with singularities. This is similar to an ant moving on the surface of a balloon that is pinched. For low energies, this problem maps to a rigid rotor and a free spin. This provides a simple example of 'emergence'.

Md Izhar Ashraf

Title: The handedness of language

Abstract: Language, which allows complex ideas to be communicated through symbolic

sequences, is a characteristic feature of our species and manifested in a multitude of forms. Using large written corpora for many different languages and scripts, we show that the occurrence probability distributions of signs at the left and right ends of words have a distinct heterogeneous nature. Characterizing this asymmetry using quantitative inequality measures, viz. information entropy and the Gini index, we show that the beginning of a word is less restrictive in sign usage than the end. This property is not simply attributable to the use of common affixes as it is seen even when only word roots are considered. We use the existence of this asymmetry to infer the direction of writing in undeciphered inscriptions that agrees with the archaeological evidence. Unlike traditional investigations of phonotactic constraints which focus on language-specific patterns, our study reveals a property valid across languages and writing systems. As both language and writing are unique aspects of our species, this universal signature may reflect an innate feature of the human cognitive phenomenon

Rahul Siddharthan

Title: Finding frequent misspelled words in a text

Abstract: A lot of problems in computational biology start life as basic problems in computer science, then evolve to encompass the complexity of real biology. I will introduce one such example, of motifs in DNA (short “words” that occur with varied spellings). The talk will be pedagogical, touching finally on some recent work.

SCHEDULE April 9, 2018

Speaker | Title | |

10:00 | Amritanshu Prasad | Knuth's Moves on Timed Words |

10:15 | Ramanathan S Thinniyam | Graph Orders |

10:30 | Tanmay Mitra | How does our immune system evolve as we age? - Disentangling novel relations among components of mature and immature human immune system |

10:45 | Parameswaran Sankaran | Orthogonal multiplication. |

11:00 | Aradhana Singh | Modular networks with bipartite communities: A model for the spread of sexually transmitted diseases in a population |

11:15 | Meena Mahajan | The right side of the (hyper) plane ... |

11:30 | Coffee break | |

12:00 | R. P. Vivek-Ananth | Prediction and analysis of the secretome of an opportunistic fungal pathogen |

12:15 | Abinash Kumar Nayak | Is weak interaction purely left handed? |

12:30 | Venkatesh Raman | Is there a majority in the house? |

12:45 | KN Raghavan | Biometric shadow of the Kostant filtration |

13:00 | Director’s Lunch | |

14:30 | Digjoy Paul | A bijective proof of the Erdos-Gallai criterion |

14:45 | Anirban Karan | Using indirect CP asymmetry to measure T and CPT violation in $B^0-\bar{B}^0$ mixing |

15:00 | Varuni Prabhakar | Moving towards the light, together |

15:15 | R Ramanujam | Catching the bad guy, with imperfect information |

15:30 | Coffee break | |

16:00 | Sruthy Murali | Planar algebra and some applications |

16:15 | G. Baskaran | Two and a Twist Springs Surprises |

16:30 | Shilpa Kastha | Testing the multipolar structure of compact binary spacetime |

16:45 | S Viswanath | How many different embeddings ? |

ABSTRACTS

Amritanshu Prasad

Title: Knuth's Moves on Timed Words

Abstract: For words in an ordered alphabet, the length of the longest increasing subword can be determined by an algorithm due to Schensted. This algorithm produces a combinatorial object called a Semistandard Young Tableau. The length of the longest increasing subword is the length of the first row of this tableau. Knuth identified two simple relations, or "moves" on words such that two words have the same Schensted tableau precisely when one can be obtained from the other by a sequence of such moves. Using Knuth's moves, Greene provided an interpretation for the lengths of the remaining rows of Schensted's tableau. Lascoux and Schuetzenberger used Knuth's moves to define the plactic monoid, which led to the first complete proof of the Littlewood-Richardson rule, a masterpiece in algebraic combinatorics.

Alur and Dill introduced timed automata to model the behavior of real-time systems. Where finite automata accept words as inputs, timed automata accept timed words, where each letter of the word comes with a time stamp. I will explain how I generalized the algorithm of Schensted, the theorem of Greene, and the plactic monoid to timed words. The only difficulty was to identify the analogues of Knuth's moves for timed words.

Ramanathan S Thinniyam

Title : Graph Orders

Abstract : Consider G, the set of all finite graphs. Many relations such as induced subgraph and subgraph form partial orders on G. First order logic over such structures (G, <=) aka graph orders, provides a language in which to formally write many theorems of graph theory. We show that this language can express any concept about graphs which is computable. We draw a parallel between graph orders and (N,+,x) i.e. natural number arithmetic; and conclude with the open question of obtaining a Matiyasevic-Robinson-Davis-Putnam theorem for graphs.

Tanmay Mitra

Title: How does our immune system evolve as we age? - Disentangling novel relations among components of mature and immature human immune system

Abstract: A salient characteristic of the human immune system is that it adapts over time in response to foreign antigens and distress signals. While a newborn child is practically sterile, with very few compartments of immune memory cells, adults are more likely to have had considerable exposure to a plethora of stimuli. Consequently, one expects an evolution of memory components in an adult's adaptive immune system. In addition, new interactions between immune cells are established over time, leading to a dynamically evolving topology for the immune cell interaction network. In this work, we aim to uncover the genetic, environmental and developmental signatures of this network, as well as possible novel clusters, by analyzing the populations of various cell types in umbilical cord and adult blood samples. We find that most of the correlations among several immune cell compartments converge during maturation. We also find that the cord and adult blood samples form two distinct clusters in PCA space, even when ignoring memory cell types, and observe unexpected interactions among different immune cell types. Our results suggest a robust evolution of the population network as development progresses.

Parameswaran Sankaran

Title: Orthogonal multiplication.

Abstract: Brahmagupta discovered the identity:

(x_1^2 + x_2^2) (y_1^2 + y_2^2) = (x_1 y_1 - x_2 y_2)^2 + (x_1 y_2 + x_2 y_1)^2

We will see generalizations of this identity and their relation to some problems in topology.

Aradhana Singh

Title: Modular networks with bipartite communities: A model for the spread of

sexually transmitted diseases in a population

Abstract: The realization that the connection topology of social networks plays a crucial role in determining the spread of infectious diseases has resulted in an enormous growth of studies in this topic. One of the specific features investigated in this context is the impact on epidemics of mesoscopic structural features, such as the organization of networks into communities (characterized by dense intra-connectivity and relatively sparse inter-connectivity). However, if one considers the class of sexually transmitted diseases (STDs), we need to necessarily take into account a further structural feature, viz., the segregation of each community into male and female subpopulations. Interactions could be primarily between the two subpopulations resulting in a nearly bipartite organization in each community. This will result in a connection topology that is modular at one scale, and anti-modular in another. We present a model for such an interaction topology, which allows us to investigate the behavior of spreading processes in such networks as a function of their mesoscopic organization. We find that disease spreading in such a system occurs at three distinct scales, viz, within each gender in a community, between two genders in a community and globally over the entire population, respectively. As STDs constitute a persistent challenge to public health, especially after the advent of HIV AIDS in the 1980s, understanding the distinct pattern of spreading of such diseases may be an important step towards their eventual control and containment.

Meena Mahajan

Title : The right side of the (hyper) plane ...

Abstract : You need the value of a function on some input. But the input is hidden from you! You can only "probe" it through queries of the form "Is it in this half-space?" Which half-spaces should you query? Sequentially or simultaneously? Do the half-space weights matter?

Some answers, and some more questions …

R. P. Vivek-Ananth

Title: Prediction and analysis of the secretome of an opportunistic fungal pathogen

Abstract: Aspergillus fumigatus and multiple other Aspergillus species cause a wide range of lung infections, collectively termed aspergillosis. Aspergilli are ubiquitous in environment with

healthy immune systems routinely eliminating inhaled conidia, however, Aspergilli can become

an opportunistic pathogen in immune-compromised patients. The aspergillosis mortality rate and

emergence of drug-resistance reveals an urgent need to identify novel targets. Secreted and cell

membrane proteins play a critical role in fungal-host interactions and pathogenesis. Using a

computational pipeline integrating data from high-throughput experiments and bioinformatic

predictions, we have identified secreted and cell membrane proteins in ten Aspergillus species

known to cause aspergillosis. Small secreted and effector-like proteins similar to agents of

fungal-plant pathogenesis were also identified within each secretome. A comparison with

humans revealed that at least 70% of Aspergillus secretomes have no sequence similarity with

the human proteome. An analysis of antigenic qualities of Aspergillus proteins revealed that the

secretome is significantly more antigenic than cell membrane proteins or the complete proteome.

Finally, overlaying an expression dataset, four A. fumigatus proteins upregulated during infection

and with available structures, were found to be structurally similar to known drug target proteins

in other organisms, and were able to dock in silico with the respective drug.

Abinash Kumar Nayak

Title: Is weak interaction purely left handed?

Abstract: The standard model is a theory describing three of the four fundamental forces of nature(i.e. electromagnetic, weak and strong). Though it has enjoyed great success in providing experimental predictions, it has failed in explaining certain observed phenomena of the universe e.g. baryon asymmetry, dark matter, dark energy, neutrino oscillations etc. Hence the next logical step is to find a new theory e.g. SUSY or improve upon the standard model thorough various phenomenological extensions e.g. left-right symmetric theory, lepto-quark models, multiple higgs models etc.. Right-handed currents are one simple extension of the standard model in allowing right handed weak currents. We propose a method to look for these currents in certain rare decay modes and with the present data we find a 5-sigma evidence of its presence.

Venkatesh Raman

Title: Is there a majority in the house?

Abstract: While this is a pressing question in the TN assembly, we will look at how a computer algorithm can find this out. A simple algorithm will line up the members, get their votes, and count them. All this can be done in linear time over a single pass.

But what if the candidates do not specify their vote (for the fear of being kidnapped), but all you can do is, by talking to pairs of them, find out if they will be voting for the same party/group? In this case, can you determine if there is a majority in the house, and if so how many pairs of them should you talk to? What if there are only two parties and you need to determine whether there is a majority? How many pairs should you talk to? What if we are interested in determining not if there is a majority, but a party that has the maximum votes?

We will look at some algorithms, and more importantly strategies to show that some of these bounds are optimal.

KN Raghavan

Title: Biometric shadow of the Kostant filtration

Abstract: Imagine a method of data compression that compresses by a large factor but is nevertheless lossless. Passing from a representation to its character is such a method. The lossless-ness is expressed by saying "the character characterizes the representation". Moreover, the method is "homomorphic" in the sense that operations on representations cast their shadows (which are operations) on characters. But, unfortunately, recovering a representation from its character is easier said than done.

The "path model" is another homomorphic lossless compression method. The factor by which it compresses is only slightly smaller than that for characters, but it has better recovery properties (than the character). Tensor product at the level of representations casts concatenation product as its shadow on paths. There is a filtration by "Kostant submodules" of the tensor product of two irreducible representations. We detect the shadow this filtration casts on paths. This is joint work with Mrigendra and Viswanath.

Digjoy Paul

Title: A bijective proof of the Erdos-Gallai criterion

Abstract: A bijective correspondence of Burge in algebraic combinatorics associates a simple graph to a semistandard Young tableau. This provides a criterion equivalent to the Erdos-Gallai

theorem, which solves the degree realization problem in Graph theory, i.e., it gives a necessary and sufficient condition for a finite sequence of natural numbers to be the degree sequence of a simple graph.

Anirban Karan

Title: Using indirect CP asymmetry to measure T and CPT violation in $B^0-\bar{B}^0$ mixing

Abstract: CPT invariance is believed to be a sacred symmetry of nature and all physical processes are supposed to obey it. Therefore, it is very important to test the validity of this assumption experimentally. We know that quantum field theory (QFT) is Lorentz invariant by construction, and hence CPT invariant too. So, to test CPT conservation, we should look for some processes where use of QFT is superfluous and simple quantum mechanics is enough. Mixing of $B^0-\bar{B}^0$ is one of such modes. I shall explain how the time-dependent, indirect CP asymmetries ($A^f_{CP/CPT}$) can be used to measure T and CPT violation in $B^0-\bar{B}^0$ mixing.

Varuni Prabhakar

Title: Moving towards the light, together

Abstract: Many micro-organisms are motile and can move towards or away from a host of stimuli. Cyanobacteria are a diverse group of photosynthetic bacteria that exhibit phototaxis, or motion in response to light. Even though cells can respond individually to light, colonies are observed to move collectively towards the light source in dense finger-like projections from colonies. We suggest an agent-based model for cyanobacterial phototaxis that accounts for slime deposition as well as for direct physical links between bacteria. Our model reproduces the experimentally observed aggregation of cells and describes the changes in colony morphology that occur as cells move towards light. Such models are part of a class of models that demonstrate how individual or local properties can result in emergent phenomena that are observable at a larger scale.

R Ramanujam

Title: Catching the bad guy, with imperfect information

Abstract: Before we begin a game, we make deals, and during play, you renege. While you can get away with it in one-shot games, `Folk Theorems' assure us that you will surely be caught out in repeated play. This works when players have perfect information, but when players have only partial views, it is hard to tell who is deviating when, even with repeated play. All this is closely related to fault tolerance in distributed computing. The problem is generally undecidable, and we

identify some decidable subclasses.

Sruthy Murali

Title: Planar algebra and some applications

Abstract: The spin planar algebra is a familiar and simple planar algebra which is known from the very first paper of Jones on planar algebras.In this talk I will discuss some applications of this planar algebra.

G. Baskaran

Title: Two and a Twist Springs Surprises

Abstract: Aristotle said, `The whole becomes more than the sum of its part'. It is true in science, arts, life etc. Two identical periodic patterns, when superimposed produce fascinating new patterns called Moire patterns. Graphene is a stable hexagonal net of carbon atoms. Graphene is a poor conductor of electricity. Put two graphene sheets directly on top of each other (perfect atomic registry), followed by a tiny twist of 1.7 degree and gate it. It turns into a superconductor, which offers zero resistance to electrical current flow. Moire pattern influences quantum dynamics of electrons, in an exciting fashion [1].

[1] G, Baskaran, arXiv:1804.000627

Shilpa Kastha

Title: Testing the multipolar structure of compact binary spacetime

Abstract: Present day parameter estimation schemes of gravitational wave events are developed based on the waveforms predicted solely by general relativity (GR). Various astrophysical observations so far have supported GR with extremely good accuracies. But there are a few alternative theories that suggest different waveforms from GR predictions as well. Since chirping signal from compact binary carries signature of gravity in the strong field regime, detection of these signals give an wide platform to test the fundamental predictions of GR. We propose a method to test the multipole structure of GR in a model independent way from GW signals for various present day detectors and upcoming ones. We associate different free parameters to different GR multipole moments appearing in the post-Newtonian phasing formula to capture the effect of alternatives theories generically and study the numerical bounds on these parameters along with the usual parameters such as masses of the binary.

S Viswanath

Title: How many different embeddings ?

Abstract: Given, two finite dimensional simple Lie algebras L and M, we would like to know if L can be embedded in M, and if so, in how many different ways ? This problem was solved by Borel-de Siebenthal and Dynkin in the 1950s. We consider the analogous problem when L and M are certain infinite dimensional Lie algebras of interest in physics, namely the hyperbolic “overextensions” of the Lie algebras sl_2 and E_8. It turns out there is a unique embedding, upto the (obvious) operations of reflection and negation.